Publications by authors named "Junling Ma"

50 Publications

The Effect of Harvesting Adults on the Evolution of Reproduction Age Via Density-Dependent Juvenile Mortality.

Bull Math Biol 2021 Sep 8;83(10):108. Epub 2021 Sep 8.

Center for Applied Mathematics, Guangzhou University, Guangzhou, 510320, Guangdong, China.

In this paper, we used a generic two-stage population model to derive an adaptive dynamical system for the evolution of reproduction age and studied how this evolution is driven by the harvest of adults. We considered the tradeoffs between maturation rate and fecundity, juvenile mortality, and adult mortality. We analyzed the benefit and cost of faster maturation under each tradeoff that drives the evolution. We found that harvesting adults affects the evolution of maturation by affecting the benefit. For the tradeoff between maturation and juvenile mortality, harvesting adults does not affect the benefit and thus, does not affect optimal maturation strategy. For the other two tradeoffs, harvesting adults affects the benefit through the equilibrium adult/juvenile ratio, which is determined by the density dependence of juveniles. Harvesting adults causes a slower maturation only if it significantly reduces this ratio, which can only happen with very strong adult protection to juveniles. Otherwise, harvesting adults always causes a faster maturation.
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http://dx.doi.org/10.1007/s11538-021-00940-1DOI Listing
September 2021

Estimating the quarantine failure rate for COVID-19.

Infect Dis Model 2021 23;6:924-929. Epub 2021 Jul 23.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

Quarantine is a crucial control measure in reducing imported COVID-19 cases and community transmissions. However, some quarantined COVID-19 patients may show symptoms after finishing quarantine due to a long median incubation period, potentially causing community transmissions. To assess the recommended 14-day quarantine policy, we develop a formula to estimate the quarantine failure rate from the incubation period distribution and the epidemic curve. We found that the quarantine failure rate increases with the exponential growth rate of the epidemic curve. We apply our formula to United States, Canada, and Hubei Province, China. Before the lockdown of Wuhan City, the quarantine failure rate in Hubei Province is about 4.1. If the epidemic curve flattens or slowly decreases, the failure rate is less than 2.8. The failure rate in US may be as high as 8.3-11.5 due to a shorter 10-day quarantine period, while the failure rate in Canada may be between 2.5 and 3.9. A 21-day quarantine period may reduce the failure rate to 0.3-0.5.
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http://dx.doi.org/10.1016/j.idm.2021.07.002DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8299156PMC
July 2021

Effect of the ratio of vessel-specific volume to fractional myocardial mass on fractional flow reserve.

Exp Biol Med (Maywood) 2021 Jul 8:15353702211027119. Epub 2021 Jul 8.

Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, China.

This study aimed to examine whether the ratio of vessel-specific coronary arterial lumen volume to the fraction of myocardial mass (V/M) affects myocardial ischemia. We proposed a calculation method for V/M, and compared the ratio of total epicardial coronary arterial lumen volume to left ventricular myocardial mass (V/M) with V/M in predicting myocardial ischemia. V/M and V/M were computed using data from 205 patients with 241 stenosis vessel who underwent coronary computed tomography angiography (CTA), quantitative coronary angiography, and fractional flow reserve. The vessel-specific coronary arterial lumen volume (V) was obtained from CTA by segmenting the coronary arterial lumen volume, while the vessel-specific fraction of myocardial mass (M) was obtained by allometric scaling. The V/M was then calculated. The cut-off values of V/M (23.55 mm/g) and V/M (12.98 mm/g) were used to define equal groups of ischemic and non-ischemic patients, respectively. Using these cut-off values, the accuracy, specificity, sensitivity, positive predictive value, and negative predictive value of V/M were 60%, 76%, 45%, 57%, and 66%, and of V/M were 87%, 92%, 77%, 89%, and 83%, respectively. Patients have different V/M values in different stenotic coronary arteries. Clinically, V/M is a quantitative indicator of the risk of myocardial ischemia.
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http://dx.doi.org/10.1177/15353702211027119DOI Listing
July 2021

Backward bifurcation in within-host HIV models.

Math Biosci 2021 05 24;335:108569. Epub 2021 Feb 24.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada.

The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R is less than unity, we show theoretically and numerically that bistability for R
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http://dx.doi.org/10.1016/j.mbs.2021.108569DOI Listing
May 2021

Acceleration of plague outbreaks in the second pandemic.

Proc Natl Acad Sci U S A 2020 11 19;117(44):27703-27711. Epub 2020 Oct 19.

Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.

Historical records reveal the temporal patterns of a sequence of plague epidemics in London, United Kingdom, from the 14th to 17th centuries. Analysis of these records shows that later epidemics spread significantly faster ("accelerated"). Between the Black Death of 1348 and the later epidemics that culminated with the Great Plague of 1665, we estimate that the epidemic growth rate increased fourfold. Currently available data do not provide enough information to infer the mode of plague transmission in any given epidemic; nevertheless, order-of-magnitude estimates of epidemic parameters suggest that the observed slow growth rates in the 14th century are inconsistent with direct (pneumonic) transmission. We discuss the potential roles of demographic and ecological factors, such as climate change or human or rat population density, in driving the observed acceleration.
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http://dx.doi.org/10.1073/pnas.2004904117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7959508PMC
November 2020

Visualising electrochemical reaction layers: mediated vs. direct oxidation.

Phys Chem Chem Phys 2020 Jun;22(22):12422-12433

Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK.

Electrochemical treatments are widely used for 'clean up' in which toxic metals and organic compounds are removed using direct or mediated electrolysis. Herein we report novel studies offering proof of concept that spectrofluorometric electrochemistry can provide important mechanistic detail into these processes. A thin layer opto-electrochemical cell, with a carbon fibre (radius 3.5 μm) working electrode, is used to visualise the optical responses of the oxidative destruction of a fluorophore either directly, on an electrode, or via the indirect reaction of the analyte with an electrochemically formed species which 'mediates' the destruction. The optical responses of these two reaction mechanisms are first predicted by numerical simulation followed by experimental validation of each using two fluorescent probes, a redox inactive (in the electrochemical window) 1,3,6,8-pyrenetetrasulfonic acid and the redox-active derivative 8-hydroxypyrene-1,3,6-trisulfonic acid. In the vicinity of a carbon electrode held at different oxidative potentials, the contrast between indirect electro-destruction, chlorination, and direct oxidation is very obvious. Excellent agreement is seen between the numerically predicted fluorescence intensity profiles and experiment.
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http://dx.doi.org/10.1039/d0cp01904fDOI Listing
June 2020

Estimating epidemic exponential growth rate and basic reproduction number.

Authors:
Junling Ma

Infect Dis Model 2020 8;5:129-141. Epub 2020 Jan 8.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic, and is also closely related to the basic reproduction number. Estimating the growth rate from the epidemic curve can be a challenge, because of its decays with time. For fast epidemics, the estimation is subject to over-fitting due to the limited number of data points available, which also limits our choice of models for the epidemic curve. We discuss the estimation of the growth rate using maximum likelihood method and simple models.
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http://dx.doi.org/10.1016/j.idm.2019.12.009DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6962332PMC
January 2020

The influence of awareness on epidemic spreading on random networks.

J Theor Biol 2020 02 22;486:110090. Epub 2019 Nov 22.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada. Electronic address:

During an outbreak, the perceived infection risk of an individual affects his/her behavior during an epidemic to lower the risk. We incorporate the awareness of infection risk into the Volz-Miller SIR epidemic model, to study the effect of awareness on disease dynamics. We consider two levels of awareness, the local one represented by the prevalence among the contacts of an individual, and the global one represented by the prevalence in the population. We also consider two possible effects of awareness: reducing infection rate or breaking infectious edges. We use the next generation matrix method to obtain the basic reproduction number of our models, and show that awareness acquired during an epidemic does not affect the basic reproduction number. However, awareness acquired from outbreaks in other regions before the start of the local epidemic reduces the basic reproduction number. Awareness always reduces the final size of an epidemic. Breaking infectious edges causes a larger reduction than reducing the infection rate. If awareness reduces the infection rate, the reduction increases with both local and global awareness. However, if it breaks infectious edges, the reduction may not be monotonic. For the same awareness, the reduction may reach a maximum on some intermediate infection rates. Whether local or global awareness has a larger effect on reducing the final size depends on the network degree distribution and the infection rate.
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http://dx.doi.org/10.1016/j.jtbi.2019.110090DOI Listing
February 2020

Patterns of seasonal and pandemic influenza-associated health care and mortality in Ontario, Canada.

BMC Public Health 2019 Sep 6;19(1):1237. Epub 2019 Sep 6.

Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.

Background: Mathematical and statistical models are used to project the future time course of infectious disease epidemics and the expected future burden on health care systems and economies. Influenza is a particularly important disease in this context because it causes annual epidemics and occasional pandemics. In order to forecast health care utilization during epidemics-and the effects of hospitalizations and deaths on the contact network and, in turn, on transmission dynamics-modellers must make assumptions about the lengths of time between infection, visiting a physician, being admitted to hospital, leaving hospital, and death. More reliable forecasts could be be made if the distributions of times between these types of events ("delay distributions") were known.

Methods: We estimated delay distributions in the province of Ontario, Canada, between 2006 and 2010. To do so, we used encrypted health insurance numbers to link 1.34 billion health care billing records to 4.27 million hospital inpatient stays. Because the four year period we studied included three typical influenza seasons and the 2009 influenza pandemic, we were able to compare the delay distributions in non-pandemic and pandemic settings. We also estimated conditional probabilities such as the probability of hospitalization within the year if diagnosed with influenza.

Results: In non-pandemic [pandemic] years, delay distribution medians (inter-quartile ranges) were: Service to Admission 6.3 days (0.1-17.6 days) [2.4 days (-0.3-13.6 days)], Admission to Discharge 3 days (1.4-5.9 days) [2.6 days (1.2-5.1 days)], Admission to Death 5.3 days (2.1-11 days) [6 days (2.6-13.1 days)]. (Service date is defined as the date, within the year, of the first health care billing that included a diagnostic code for influenza-like-illness.) Among individuals diagnosed with either pneumonia or influenza in a given year, 19% [16%] were hospitalized within the year and 3% [2%] died in hospital. Among all individuals who were hospitalized, 10% [12%] were diagnosed with pneumonia or influenza during the year and 5% [5%] died in hospital.

Conclusion: Our empirical delay distributions and conditional probabilities should help facilitate more accurate forecasts in the future, including improved predictions of hospital bed demands during influenza outbreaks, and the expected effects of hospitalizations on epidemic dynamics.
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http://dx.doi.org/10.1186/s12889-019-7369-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6731609PMC
September 2019

Clinical efficacy of gangliosides on premature infants suffering from white matter damage and its effect on the levels of IL-6, NSE and S100β.

Exp Ther Med 2019 Jul 2;18(1):63-68. Epub 2019 May 2.

Department of Neonatology, Tianjin Central Hospital of Obstetrics and Gynecology, Tianjin 300100, P.R. China.

This study investigated the clinical efficacy of gangliosides on premature infants suffering from white matter damage and its effect on the levels of IL-6, neuron-specific enolase (NSE) and S100β. Seventy-six cases of premature infants suffering from white matter damage admitted to the Tianjin Central Hospital of Obstetrics and Gynecology from February 2016 to March 2017 were enrolled in this study. They were randomly divided into the control group and the observation group with 38 cases in each group. Control group was given conventional treatment, while the observation group was given ganglioside treatment on the basis of the treatment given to the control group. Craniocerebrum ultrasonic detection was used to observe the condition of white matter around the ventricle of child patients in the two groups, before and after treatment. ELISA was used to detect the levels of IL-6, NSE and S100β. Gesell developmental scale was used to compare the developmental quotient (DQ) of various function regions of the children. The total effective rate of the observation group was higher than that of the control group (P<0.05). The gray value of craniocerebrum ultrasonic detection in the observation group was significantly lower than that in the control group (P<0.05). IL-6, S100β and NSE levels of the child patients in the two groups were significantly declined at 7 and 14 days after birth (P<0.05). After 1 year, the observation group scored significantly higher DQ than the control group in the aspects of social adaptation, gross motor, fine motor, language and personal social contact. The sequel incidence of patients in the observation group was significantly lower than that of the control group (P<0.05). In conclusion, the intervention treatment with ganglioside for premature infants suffering from white matter damage was beneficial and provided a protective effect. It also reduced sequel and produced some promising results.
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http://dx.doi.org/10.3892/etm.2019.7539DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566046PMC
July 2019

Host contact structure is important for the recurrence of Influenza A.

J Math Biol 2018 11 4;77(5):1563-1588. Epub 2018 Jul 4.

College of Science, Shanghai University for Science and Technology, Shanghai, China.

An important characteristic of influenza A is its ability to escape host immunity through antigenic drift. A novel influenza A strain that causes a pandemic confers full immunity to infected individuals. Yet when the pandemic strain drifts, these individuals will have decreased immunity to drifted strains in the following seasonal epidemics. We compute the required decrease in immunity so that a recurrence is possible. Models for influenza A must make assumptions on the contact structure on which the disease spreads. By considering local stability of the disease free equilibrium via computation of the reproduction number, we show that the classical random mixing assumption predicts an unrealistically large decrease of immunity before a recurrence is possible. We improve over the classical random mixing assumption by incorporating a contact network structure. A complication of contact networks is correlations induced by the initial pandemic. We provide a novel analytic derivation of such correlations and show that contact networks may require a dramatically smaller loss of immunity before recurrence. Hence, the key new insight in our paper is that on contact networks the establishment of a new strain is possible for much higher immunity levels of previously infected individuals than predicted by the commonly used random mixing assumption. This suggests that stable contacts like classmates, coworkers and family members are a crucial path for the spread of influenza in human populations.
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http://dx.doi.org/10.1007/s00285-018-1263-5DOI Listing
November 2018

Edge-based epidemic spreading in degree-correlated complex networks.

J Theor Biol 2018 10 6;454:164-181. Epub 2018 Jun 6.

School of Computer and Information Technology, Shanxi University, Taiyuan 030006, People's Republic of China.

Networks that grow through the addition of new nodes or edges may acquire degree-degree correlations. When one considers a short epidemic on a slowly growing network, such as the spread of a strain of influenza in a population for one season, it is reasonable to assume that the degree-correlated network is static during the course of an epidemic. In this case using only information about the network degree distribution is not enough to capture the exponential growth phase, the epidemic peak or the final epidemic size. Hence, in this paper we formulate an edge-based SIR epidemic model on degree-correlated networks, which includes the Miller model on configuration networks as a special case. The model is relatively low-dimensional; in particular, considering the fact that it captures degree correlations. Moreover, we derive rate equations to compute two node degree correlations in a growing network. Predictions of our model agree well with the corresponding stochastic SIR process on degree-correlated networks, such as the exponential growth phase, the epidemic peak and the final epidemic size. The basic reproduction number R and the final epidemic size are theoretically derived, which are equivalent to those based on the percolation theory. However, our model has the advantage that it can trace the dynamic spread of an epidemic on degree-correlated networks. This provides us with more accurate information to predict and control the spread of diseases in growing populations with biased-mixing. Finally, our model is tested on degree-correlated networks with clustering, and it is shown that our model is robust to degree-correlated networks with small clustering.
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http://dx.doi.org/10.1016/j.jtbi.2018.06.006DOI Listing
October 2018

The effect of sexual transmission on Zika virus dynamics.

J Math Biol 2018 12 25;77(6-7):1917-1941. Epub 2018 Apr 25.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

Zika virus is a human disease that may lead to neurological disorders in affected individuals, and may be transmitted vectorially (by mosquitoes) or sexually. A mathematical model of Zika virus transmission is formulated, taking into account mosquitoes, sexually active males and females, inactive individuals, and considering both vector transmission and sexual transmission from infectious males to susceptible females. Basic reproduction numbers are computed, and disease control strategies are evaluated. The effect of the incidence function used to model sexual transmission from infectious males to susceptible females is investigated. It is proved that for such functions that are sublinear, if the basic reproduction [Formula: see text], then the disease dies out and [Formula: see text] is a sharp threshold. Moreover, under certain conditions on model parameters and assuming mass action incidence for sexual transmission, it is proved that if [Formula: see text], there exists a unique endemic equilibrium that is globally asymptotically stable. However, under nonlinear incidence, it is shown that for certain functions backward bifurcation and Hopf bifurcation may occur, giving rise to subthreshold equilibria and periodic solutions, respectively. Numerical simulations for various parameter values are displayed to illustrate these behaviours.
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http://dx.doi.org/10.1007/s00285-018-1230-1DOI Listing
December 2018

Estimation of Cross-Immunity Between Drifted Strains of Influenza A/H3N2.

Bull Math Biol 2018 03 25;80(3):657-669. Epub 2018 Jan 25.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

To determine the cross-immunity between influenza strains, we design a novel statistical method, which uses a theoretical model and clinical data on attack rates and vaccine efficacy among school children for two seasons after the 1968 A/H3N2 influenza pandemic. This model incorporates the distribution of susceptibility and the dependence of cross-immunity on the antigenic distance of drifted strains. We find that the cross-immunity between an influenza strain and the mutant that causes the next epidemic is 88%. Our method also gives estimates of the vaccine protection against the vaccinating strain, and the basic reproduction number of the 1968 pandemic influenza.
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http://dx.doi.org/10.1007/s11538-018-0395-5DOI Listing
March 2018

An edge-based SIR model for sexually transmitted diseases on the contact network.

J Theor Biol 2018 02 12;439:216-225. Epub 2017 Dec 12.

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China. Electronic address:

Sexually transmitted diseases, which are infections through sexual contact, pose severe public health threat nowadays. In this paper, we develop a novel model for such diseases on a bipartite random contact network. Our model is precise with arbitrary initial conditions, which makes it suitable to study preventative vaccination strategies. We derive the reproduction number and show that R=1 is the disease threshold. An implicit formula for the final epidemic size is also derived, and we show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We find that the final size in either sex is heavily influenced by the degree distribution of the opposite sex.
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http://dx.doi.org/10.1016/j.jtbi.2017.12.003DOI Listing
February 2018

antibody responses in association with eradication outcome and recurrence: a population-based intervention trial with 7.3-year follow-up in China.

Chin J Cancer Res 2017 Apr;29(2):127-136

Key Laboratory of Carcinogenesis and Translational Research (Ministry of Education/Beijing), Department of Cancer Epidemiology, Peking University Cancer Hospital & Institute, Beijing 100142, China.

Objective: To identify serum biomarkers that may predict the short or long term outcomes of anti- () treatment, a follow-up study was performed based on an intervention trial in Linqu County, China.

Methods: A total of 529 subjects were selected randomly from 1,803 participants to evaluate total anti- immunoglobulin G (IgG) and 10 specific antibody levels before and after treatment at 1-, 2- and 7.3-year. The outcomes of anti- treatment were also parallelly assessed byC-urea breath test at 45-d after treatment and 7.3-year at the end of follow-up.

Results: We found the medians of anti- IgG titers were consistently below cut-off value through 7.3 years in eradicated group, however, the medians declined in recurrence group to 1.2 at 1-year after treatment and slightly increased to 2.0 at 7.3-year. While the medians were significantly higher (>3.0 at 2- and 7.3-year) among subjects who failed the eradication or received placebo. For specific antibody responses, baseline seropositivities of FliD and HpaA were reversely associated with eradication failure [for FliD, odds ratio (OR)=0.44, 95% confidence interval (95% CI): 0.27-0.73; for HpaA, OR=0.32, 95% CI: 0.17-0.60]. The subjects with multiple positive specific antibodies at baseline were more likely to be successfully eradicated in a linear fashion (P=0.006).

Conclusions: Our study suggested that total anti- IgG level may serve as a potential monitor of long-term impact on anti- treatment, and priority for treatment may be endowed to the subjects with multiple seropositive antibodies at baseline, especially for FliD and HapA.
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http://dx.doi.org/10.21147/j.issn.1000-9604.2017.02.05DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5422414PMC
April 2017

Estimation of Zika virus prevalence by appearance of microcephaly.

BMC Infect Dis 2016 Dec 12;16(1):754. Epub 2016 Dec 12.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

Background: There currently is a severe Zika Virus (ZIKV) epidemic in Brazil and other South American countries. Due to international travel, this poses severe public health risk of ZIKV importation to other countries. We estimate the prevalence of ZIKV in an import region by the time a microcephaly case is detected, since microcephaly is presently the most significant indication of ZIKV presence.

Methods: We establish a mathematical model to describe ZIKV spread from a source region to an import region. This model incorporates both vector transmission (between humans and mosquitoes) and sexual transmission (from males to females). We take account of population structure through a contact network for sexually active individuals. Parameter values of our model are either taken from the literature or estimated from travel data.

Results: This model gives us the probability distribution of time until detection of the first microcephaly case. Based on current field observations, our results also indicate that the percentage of infected pregnant women that results in fetal abnormalities is more likely to be on the smaller end of the 1%-30% spectrum that is currently hypothesized. Our model predicts that for import regions with at least 250,000 people, on average 1,000-12,000 will have been infected by the time of the first detection of microcephaly, and on average 200-1,500 will be infectious at this time. Larger population sizes do not significantly change our predictions.

Conclusions: By the first detection of a microcephaly case, a sizable fraction of the population will have been infected by ZIKV. It is thus clear that adequate surveillance, isolation, and quarantine are needed in susceptible import regions to stop the dissemination of a Zika epidemic.
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http://dx.doi.org/10.1186/s12879-016-2076-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5153823PMC
December 2016

Two Redundant Receptor-Like Cytoplasmic Kinases Function Downstream of Pattern Recognition Receptors to Regulate Activation of SA Biosynthesis.

Plant Physiol 2016 06 4;171(2):1344-54. Epub 2016 Apr 4.

Department of Botany, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4 (Q.K., T.S., J.M., M.L., Y.-t.C., Q.Z., D.W., Z.Z., Y.Z.);National Institute of Biological Sciences, Beijing 102206, China (N.Q.); andCollege of Environmental and Chemical Engineering, Dalian Jiaotong University, Dalian 116028, China (J.M.)

Salicylic acid (SA) serves as a critical signaling molecule in plant defense. Two transcription factors, SARD1 and CBP60g, control SA biosynthesis through regulating pathogen-induced expression of Isochorismate Synthase1, which encodes a key enzyme for SA biosynthesis. Here, we report that Pattern-Triggered Immunity Compromised Receptor-like Cytoplasmic Kinase1 (PCRK1) and PCRK2 function as key regulators of SA biosynthesis. In the pcrk1 pcrk2 double mutant, pathogen-induced expression of SARD1, CBP60g, and ICS1 is greatly reduced. The pcrk1 pcrk2 double mutant, but neither of the single mutants, exhibits reduced accumulation of SA and enhanced disease susceptibility to bacterial pathogens. Both PCRK1 and PCRK2 interact with the pattern recognition receptor FLS2, and treatment with pathogen-associated molecular patterns leads to rapid phosphorylation of PCRK2. Our data suggest that PCRK1 and PCRK2 function downstream of pattern recognition receptor in a signal relay leading to the activation of SA biosynthesis.
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http://dx.doi.org/10.1104/pp.15.01954DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4902587PMC
June 2016

Disease invasion risk in a growing population.

J Math Biol 2016 09 21;73(3):665-81. Epub 2016 Jan 21.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada.

The spread of an infectious disease may depend on the population size. For simplicity, classic epidemic models assume homogeneous mixing, usually standard incidence or mass action. For standard incidence, the contact rate between any pair of individuals is inversely proportional to the population size, and so the basic reproduction number (and thus the initial exponential growth rate of the disease) is independent of the population size. For mass action, this contact rate remains constant, predicting that the basic reproduction number increases linearly with the population size, meaning that disease invasion is easiest when the population is largest. In this paper, we show that neither of these may be true on a slowly evolving contact network: the basic reproduction number of a short epidemic can reach its maximum while the population is still growing. The basic reproduction number is proportional to the spectral radius of a contact matrix, which is shown numerically to be well approximated by the average excess degree of the contact network. We base our analysis on modeling the dynamics of the average excess degree of a random contact network with constant population input, proportional deaths, and preferential attachment for contacts brought in by incoming individuals (i.e., individuals with more contacts attract more incoming contacts). In addition, we show that our result also holds for uniform attachment of incoming contacts (i.e., every individual has the same chance of attracting incoming contacts), and much more general population dynamics. Our results show that a disease spreading in a growing population may evade control if disease control planning is based on the basic reproduction number at maximum population size.
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http://dx.doi.org/10.1007/s00285-015-0962-4DOI Listing
September 2016

The coexistence or replacement of two subtypes of influenza.

Math Biosci 2015 Dec 8;270(Pt A):1-9. Epub 2015 Oct 8.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada. Electronic address:

A pandemic subtype of influenza A sometimes replaces but sometimes coexists with the previous seasonal subtype. For example, the 1957 pandemic subtype H2N2 replaced the seasonal subtype H1N1; whereas after 1977 subtypes H1N1 (from the pandemic) and H3N2 continue to coexist. In an attempt to understand these alternatives, a hybrid model for the dynamics of influenza A is formulated. During an epidemic season the model takes into account cross-immunity of strains depending on the most recent seasonal infection. This cross-immunity reduces susceptibility to related strains of the seasonal subtype, and wanes with time due to virus drift. The population is assumed to reach an equilibrium distribution in susceptibility after several seasons, and then a pandemic subtype appears. Individuals who have been infected by the seasonal subtype all have the same cross-immunity to the pandemic subtype. A combination of theoretical and numerical analyses shows that for very strong cross-immunity between the subtypes the pandemic cannot invade, whereas for strong and weak cross-immunity there is coexistence for the season following the pandemic, and for intermediate levels of cross-immunity the pandemic may replace the seasonal subtype. This replacement depends on the basic reproduction numbers of seasonal and pandemic influenza. Vaccination against the seasonal subtype is found to slightly increase this range for pandemic replacement, with the range increasing with increasing vaccine protection and with the length of time that vaccine-induced immunity lasts.
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http://dx.doi.org/10.1016/j.mbs.2015.09.006DOI Listing
December 2015

Survival and Stationary Distribution Analysis of a Stochastic Competitive Model of Three Species in a Polluted Environment.

Bull Math Biol 2015 Jul 20;77(7):1285-326. Epub 2015 May 20.

College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China.

In this paper, we develop and study a stochastic model for the competition of three species with a generalized dose-response function in a polluted environment. We first carry out the survival analysis and obtain sufficient conditions for the extinction, non-persistence, weak persistence in the mean, strong persistence in the mean and stochastic permanence. The threshold between weak persistence in the mean and extinction is established for each species. Then, using Hasminskii's methods and a Lyapunov function, we derive sufficient conditions for the existence of stationary distribution for each population. Numerical simulations are carried out to support our theoretical results, and some biological significance is presented.
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http://dx.doi.org/10.1007/s11538-015-0086-4DOI Listing
July 2015

Model for disease dynamics of a waterborne pathogen on a random network.

J Math Biol 2015 Oct 19;71(4):961-77. Epub 2014 Oct 19.

School of Science, Donghua University, Shanghai, 201620, China,

A network epidemic SIWR model for cholera and other diseases that can be transmitted via the environment is developed and analyzed. The person-to-person contacts are modeled by a random contact network, and the contagious environment is modeled by an external node that connects to every individual. The model is adapted from the Miller network SIR model, and in the homogeneous mixing limit becomes the Tien and Earn deterministic cholera model without births and deaths. The dynamics of our model shows excellent agreement with stochastic simulations. The basic reproduction number [Formula: see text] is computed, and on a Poisson network shown to be the sum of the basic reproduction numbers of the person-to-person and person-to-water-to-person transmission pathways. However, on other networks, [Formula: see text] depends nonlinearly on the transmission along the two pathways. Type reproduction numbers are computed and quantify measures to control the disease. Equations giving the final epidemic size are obtained.
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http://dx.doi.org/10.1007/s00285-014-0839-yDOI Listing
October 2015

The origin of segmentation motor activity in the intestine.

Nat Commun 2014 ;5:3326

Department of Medicine, Faculty of Health Sciences, Farncombe Family Digestive Health Research Institute, McMaster University, 1200 Main Street West, Hamilton, Ontario, Canada L8N3Z5.

The segmentation motor activity of the gut that facilitates absorption of nutrients was first described in the late 19th century, but the fundamental mechanisms underlying it remain poorly understood. The dominant theory suggests alternate excitation and inhibition from the enteric nervous system. Here we demonstrate that typical segmentation can occur after total nerve blockade. The segmentation motor pattern emerges when the amplitude of the dominant pacemaker, the slow wave generated by interstitial cells of Cajal associated with the myenteric plexus (ICC-MP), is modulated by the phase of induced lower frequency rhythmic transient depolarizations, generated by ICC associated with the deep muscular plexus (ICC-DMP), resulting in a waxing and waning of the amplitude of the slow wave and a rhythmic checkered pattern of segmentation motor activity. Phase-amplitude modulation of the slow waves points to an underlying system of coupled nonlinear oscillators originating in the networks of ICC.
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http://dx.doi.org/10.1038/ncomms4326DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4885742PMC
November 2015

Estimating initial epidemic growth rates.

Bull Math Biol 2014 Jan 23;76(1):245-60. Epub 2013 Nov 23.

Mathematics and Statistics, University of Victoria, Victoria, BC, Canada,

The initial exponential growth rate of an epidemic is an important measure of disease spread, and is commonly used to infer the basic reproduction number [Formula: see text]. While modern techniques (e.g., MCMC and particle filtering) for parameter estimation of mechanistic models have gained popularity, maximum likelihood fitting of phenomenological models remains important due to its simplicity, to the difficulty of using modern methods in the context of limited data, and to the fact that there is not always enough information available to choose an appropriate mechanistic model. However, it is often not clear which phenomenological model is appropriate for a given dataset. We compare the performance of four commonly used phenomenological models (exponential, Richards, logistic, and delayed logistic) in estimating initial epidemic growth rates by maximum likelihood, by fitting them to simulated epidemics with known parameters. For incidence data, both the logistic model and the Richards model yield accurate point estimates for fitting windows up to the epidemic peak. When observation errors are small, the Richards model yields confidence intervals with better coverage. For mortality data, the Richards model and the delayed logistic model yield the best growth rate estimates. We also investigate the width and coverage of the confidence intervals corresponding to these fits.
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http://dx.doi.org/10.1007/s11538-013-9918-2DOI Listing
January 2014

Epidemic dynamics on semi-directed complex networks.

Math Biosci 2013 Dec 17;246(2):242-51. Epub 2013 Oct 17.

School of Mechatronic Engineering, North University of China, Shanxi, Taiyuan 030051, People's Republic of China; Department of Mathematics, North University of China, Shanxi, Taiyuan 030051, People's Republic of China.

In this paper an SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number R0 is obtained analytically. We verify that the R0 contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if R0<1 then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally the numerical simulations holds for these analytical results are given.
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http://dx.doi.org/10.1016/j.mbs.2013.10.001DOI Listing
December 2013

Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales.

Proc Biol Sci 2013 Sep 7;280(1766):20131345. Epub 2013 Sep 7.

Department of Applied Mathematics, Hong Kong Polytechnic University Hung Hom, , Kowloon, Hong Kong (SAR), People's Republic of China.

Past influenza pandemics appear to be characterized by multiple waves of incidence, but the mechanisms that account for this phenomenon remain unclear. We propose a simple epidemic model, which incorporates three factors that might contribute to the generation of multiple waves: (i) schools opening and closing, (ii) temperature changes during the outbreak, and (iii) changes in human behaviour in response to the outbreak. We fit this model to the reported influenza mortality during the 1918 pandemic in 334 UK administrative units and estimate the epidemiological parameters. We then use information criteria to evaluate how well these three factors explain the observed patterns of mortality. Our results indicate that all three factors are important but that behavioural responses had the largest effect. The parameter values that produce the best fit are biologically reasonable and yield epidemiological dynamics that match the observed data well.
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http://dx.doi.org/10.1098/rspb.2013.1345DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3730600PMC
September 2013

Estimation of AUC or Partial AUC under Test-Result-Dependent Sampling.

Stat Biopharm Res 2012 Jan 1;4(4):313-323. Epub 2012 Oct 1.

Department of Biostatistics & Bioinformatics, Duke University Medical Center, DUMC 2717, Durham, N.C. 27710, U.S.A.

The area under the ROC curve (AUC) and partial area under the ROC curve (pAUC) are summary measures used to assess the accuracy of a biomarker in discriminating true disease status. The standard sampling approach used in biomarker validation studies is often inefficient and costly, especially when ascertaining the true disease status is costly and invasive. To improve efficiency and reduce the cost of biomarker validation studies, we consider a test-result-dependent sampling (TDS) scheme, in which subject selection for determining the disease state is dependent on the result of a biomarker assay. We first estimate the test-result distribution using data arising from the TDS design. With the estimated empirical test-result distribution, we propose consistent nonparametric estimators for AUC and pAUC and establish the asymptotic properties of the proposed estimators. Simulation studies show that the proposed estimators have good finite sample properties and that the TDS design yields more efficient AUC and pAUC estimates than a simple random sampling (SRS) design. A data example based on an ongoing cancer clinical trial is provided to illustrate the TDS design and the proposed estimators. This work can find broad applications in design and analysis of biomarker validation studies.
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http://dx.doi.org/10.1080/19466315.2012.692514DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3564679PMC
January 2012

The importance of contact network topology for the success of vaccination strategies.

J Theor Biol 2013 May 29;325:12-21. Epub 2013 Jan 29.

Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4.

The effects of a number of vaccination strategies on the spread of an SIR type disease are numerically investigated for several common network topologies including random, scale-free, small world, and meta-random networks. These strategies, namely, prioritized, random, follow links and contact tracing, are compared across networks using extensive simulations with disease parameters relevant for viruses such as pandemic influenza H1N1/09. Two scenarios for a network SIR model are considered. First, a model with a given transmission rate is studied. Second, a model with a given initial growth rate is considered, because the initial growth rate is commonly used to impute the transmission rate from incidence curves and to predict the course of an epidemic. Since a vaccine may not be readily available for a new virus, the case of a delay in the start of vaccination is also considered in addition to the case of no delay. It is found that network topology can have a larger impact on the spread of the disease than the choice of vaccination strategy. Simulations also show that the network structure has a large effect on both the course of an epidemic and the determination of the transmission rate from the initial growth rate. The effect of delay in the vaccination start time varies tremendously with network topology. Results show that, without the knowledge of network topology, predictions on the peak and the final size of an epidemic cannot be made solely based on the initial exponential growth rate or transmission rate. This demonstrates the importance of understanding the topology of realistic contact networks when evaluating vaccination strategies.
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http://dx.doi.org/10.1016/j.jtbi.2013.01.006DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7094094PMC
May 2013

ROC curve estimation under test-result-dependent sampling.

Biostatistics 2013 Jan 20;14(1):160-72. Epub 2012 Jun 20.

Department of Biostatistics & Bioinformatics, Duke University Medical Center, Durham, NC 27710, USA.

The receiver operating characteristic (ROC) curve is often used to evaluate the performance of a biomarker measured on continuous scale to predict the disease status or a clinical condition. Motivated by the need for novel study designs with better estimation efficiency and reduced study cost, we consider a biased sampling scheme that consists of a SRC and a supplemental TDC. Using this approach, investigators can oversample or undersample subjects falling into certain regions of the biomarker measure, yielding improved precision for the estimation of the ROC curve with a fixed sample size. Test-result-dependent sampling will introduce bias in estimating the predictive accuracy of the biomarker if standard ROC estimation methods are used. In this article, we discuss three approaches for analyzing data of a test-result-dependent structure with a special focus on the empirical likelihood method. We establish asymptotic properties of the empirical likelihood estimators for covariate-specific ROC curves and covariate-independent ROC curves and give their corresponding variance estimators. Simulation studies show that the empirical likelihood method yields good properties and is more efficient than alternative methods. Recommendations on number of regions, cutoff points, and subject allocation is made based on the simulation results. The proposed methods are illustrated with a data example based on an ongoing lung cancer clinical trial.
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http://dx.doi.org/10.1093/biostatistics/kxs020DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3577107PMC
January 2013

Edge removal in random contact networks and the basic reproduction number.

J Math Biol 2013 Aug 23;67(2):217-38. Epub 2012 May 23.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada.

Understanding the effect of edge removal on the basic reproduction number R0 for disease spread on contact networks is important for disease management. The formula for the basic reproduction number R0 in random network SIR models of configuration type suggests that for degree distributions with large variance, a reduction of the average degree may actually increase R0. To understand this phenomenon, we develop a dynamical model for the evolution of the degree distribution under random edge removal, and show that truly random removal always reduces R0. The discrepancy implies that any increase in R0 must result from edge removal changing the network type, invalidating the use of the basic reproduction number formula for a random contact network. We further develop an epidemic model incorporating a contact network consisting of two groups of nodes with random intra- and inter-group connections, and derive its basic reproduction number. We then prove that random edge removal within either group, and between groups, always decreases the appropriately defined R0. Our models also allow an estimation of the number of edges that need to be removed in order to curtail an epidemic.
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http://dx.doi.org/10.1007/s00285-012-0545-6DOI Listing
August 2013
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