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Adv Differ Equ 2021 30;2021(1):354. Epub 2021 Jul 30.

School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, Canada.

Hahn's difference operator , , , is used to unify the recently established difference and -asymptotic iteration methods (DAIM, AIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the -hypergeometric equation. Read More

Adv Differ Equ 2021 30;2021(1):478. Epub 2021 Oct 30.

Dpto. Matemática Aplicada, ETSI Industriales, Universidad Politécnica de Madrid, Madrid, Spain.

The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviors, or others. To include a sufficiently general disease model, we first build up from first principles a discrete-time susceptible-exposed-infectious-recovered-susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number . Read More

Adv Differ Equ 2021 26;2021(1):473. Epub 2021 Oct 26.

Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Read More

Adv Differ Equ 2021 20;2021(1):468. Epub 2021 Oct 20.

Department of Mathematics, Technische Universitat Chemnitz, Chemnitz, Germany.

Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. Read More

Adv Differ Equ 2021 18;2021(1):457. Epub 2021 Oct 18.

Department of Mathematics, College of Natural and Computational Sciences, Haramaya University, Dire Dawa, Ethiopia.

In this paper, we formulate an deterministic model and extend it to a stochastic model by introducing intensity of stochastic factors and Brownian motion. Our basic qualitative analysis of both models includes the positivity of the solution, invariant region, disease-free equilibrium point, basic reproduction number, local and global stability of disease-free equilibrium point, endemic equilibrium point, and sensitivity. We obtain the stochastic reproduction number and local stability by using twice differentiable Itô's formula. Read More

Adv Differ Equ 2021 9;2021(1):443. Epub 2021 Oct 9.

Faculty of Science and Technology, University of the Basque Country, 644 de Bilbao, Leioa, 48080 Bilbao Spain.

The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Read More

Adv Differ Equ 2021 2;2021(1):435. Epub 2021 Oct 2.

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box: 47416-95447, Babolsar, Iran.

In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. Read More

Adv Differ Equ 2021 23;2021(1):424. Epub 2021 Sep 23.

School of Mathematics, Iran University of Science and Technology, 16844 Tehran, Iran.

In this article, by using the Herman-Pole technique the conservation laws of the Jimbo-Miwa equation are obtained, and then by using the Lie symmetry analysis all of the geometric vector fields of this equation are given. Also, the non-classical symmetries of the Jimbo-Miwa equation have been determined by applying nonclassical schemes. Eventually, the ansatz solutions of the Jimbo-Miwa equations utilizing the tanh technique have been offered. Read More

Adv Differ Equ 2021 24;2021(1):395. Epub 2021 Aug 24.

Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.

Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana-Baleanu-Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability are formulated for the problem under consideration. Read More

Adv Differ Equ 2021 19;2021(1):387. Epub 2021 Aug 19.

Mathematics Department, City University of Science and Information Technology, Peshawar, Pakistan.

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. Read More

Adv Differ Equ 2021 3;2021(1):363. Epub 2021 Aug 3.

Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Read More

Adv Differ Equ 2021 31;2021(1):360. Epub 2021 Jul 31.

School of Mathematics, Hefei Normal University, Hefei, 230039 P.R. China.

In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson's dual system with harvesting terms. By means of the continuation coincidence degree theorem, a set of sufficient conditions, which ensure that there exists at least one positive periodic solution, are established. A numerical example with graphical simulation of the model is provided to examine the validity of the main results. Read More

Adv Differ Equ 2021 29;2021(1):351. Epub 2021 Jul 29.

IEEE, 94086547, Kuala Lumpur, 59200 Malaysia.

There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. Read More

Adv Differ Equ 2021 20;2021(1):341. Epub 2021 Jul 20.

School of Advanced Sciences & Languages, Department of Mathematics, VIT Bhopal University, Kottri Kalan (Village), 466 114 Sehore (District), Madhya Pradesh India.

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from  03, 2020 to  29, 2021 which is a data range of more than one complete year. We propose a Atangana-Baleanu type fractional-order model and simulate it by using predictor-corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. Read More

Adv Differ Equ 2021 16;2021(1):337. Epub 2021 Jul 16.

Department of Mathematics and Applied Mathematics, University of the Western Cape, Robert Sobukwe Rd, Bellville, 7530 South Africa.

We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. Read More

Adv Differ Equ 2021 3;2021(1):319. Epub 2021 Jul 3.

Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.

This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number ; a disease-free equilibrium and a disease endemic equilibrium . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number , we show that the endemic equilibrium state is locally asymptotically stable if . Read More

Adv Differ Equ 2021 15;2021(1):293. Epub 2021 Jun 15.

Department of Basic Sciences, Common First Year, King Saud University, Riyadh, 11451 Saudi Arabia.

This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Read More

Adv Differ Equ 2021 12;2021(1):288. Epub 2021 Jun 12.

Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia.

In this paper, we discuss the basic reproduction number of stochastic epidemic models with random perturbations. We define the basic reproduction number in epidemic models by using the integral of a function or survival function. We study the systems of stochastic differential equations for SIR, SIS, and SEIR models and their stability analysis. Read More

Adv Differ Equ 2021 12;2021(1):287. Epub 2021 Jun 12.

School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021 P.R. China.

Recently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Read More

Adv Differ Equ 2021 11;2021(1):285. Epub 2021 Jun 11.

Cheikh Anta Diop University, Dakar, Senegal.

In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. Read More

Adv Differ Equ 2021 25;2021(1):270. Epub 2021 May 25.

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. Read More

Adv Differ Equ 2021 14;2021(1):253. Epub 2021 May 14.

Department of Mathematics, College of Sciences, King Saud University, Riyadh, Kingdom of Saudi Arabia.

In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease () in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk and high-risk susceptible individuals; the compartment of exposed individuals ; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals and the one consisting of infected diagnosed individuals ); the compartment of recovered undiagnosed individuals , that of recovered diagnosed individuals, and the compartment of extinct individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. Read More

Adv Differ Equ 2021 1;2021(1):228. Epub 2021 May 1.

Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634 USA.

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. Read More

Adv Differ Equ 2021 12;2021(1):202. Epub 2021 Apr 12.

School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.

We introduce a mathematical model, namely, ∗-fuzzy measure model for COVID-19 disease and consider some properties of ∗-fuzzy measure such as Lebesque-Radon-Nikodym theorem. Read More

Adv Differ Equ 2021 8;2021(1):200. Epub 2021 Apr 8.

College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830017 P.R. China.

In this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Read More

Adv Differ Equ 2021 30;2021(1):191. Epub 2021 Mar 30.

School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, China.

In this manuscript, we investigate a novel Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical quarantine rate in this model. Firstly, we analyze the existence of an equilibrium, including a virus-free equilibrium and a virus-existence equilibrium. Then local stability and the occurrence of Hopf bifurcation have been researched by thinking of time delay as the bifurcation parameter. Read More

Adv Differ Equ 2021 24;2021(1):185. Epub 2021 Mar 24.

Department of Mathematics, Cankaya University, Öǧretmenler Cad. 1406530, Ankara, Turkey.

Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Read More

Adv Differ Equ 2021 24;2021(1):184. Epub 2021 Mar 24.

Department of Mathematics, University of Malakand, Chakdara, Dir(L), KPK Pakistan.

This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo-Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Read More

Adv Differ Equ 2021 19;2021(1):174. Epub 2021 Mar 19.

Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, Ethiopia.

We consider a SEAIR epidemic model with Atangana-Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Read More

Adv Differ Equ 2021 19;2021(1):172. Epub 2021 Mar 19.

School of Mathematics and Information Science, North Minzu University, Yinchuan, China.

In this paper, we investigate the dynamical behavior of a two-group SVIR epidemic model with random effect. Firstly, the two-group SVIR epidemic model with random perturbation of natural death rate is established. The existence and uniqueness of positive solution are proved by using stopping time theory and the Lyapunov analysis method. Read More