# Publications by authors named "Hossam M Ezzat"

2 Publications

• Page 1 of 1

### Lyapunov function and global asymptotic stability for a new multiscale viral dynamics model incorporating the immune system response: Implemented upon HCV.

##### Authors:
Hesham A Elkaranshawy Hossam M Ezzat Nermeen N Ibrahim

PLoS One 2021 12;16(10):e0257975. Epub 2021 Oct 12.

High Institute of Public Health, Alexandria University, Alexandria, Egypt.

In this paper, a new mathematical model is formulated that describes the interaction between uninfected cells, infected cells, viruses, intracellular viral RNA, Cytotoxic T-lymphocytes (CTLs), and antibodies. Hence, the model contains certain biological relations that are thought to be key factors driving this interaction which allow us to obtain precise logical conclusions. Therefore, it improves our perception, that would otherwise not be possible, to comprehend the pathogenesis, to interpret clinical data, to control treatment, and to suggest new relations. This model can be used to study viral dynamics in patients for a wide range of infectious diseases like HIV, HPV, HBV, HCV, and Covid-19. Though, analysis of a new multiscale HCV model incorporating the immune system response is considered in detail, the analysis and results can be applied for all other viruses. The model utilizes a transformed multiscale model in the form of ordinary differential equations (ODE) and incorporates into it the interaction of the immune system. The role of CTLs and the role of antibody responses are investigated. The positivity of the solutions is proven, the basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed based on the Lyapunov invariance principle. By using appropriate Lyapunov functions, the uninfected equilibrium point is proven to be globally asymptotically stable when the reproduction number is less than one and unstable otherwise. Global stability of the infected equilibrium points is considered, and it has been found that each equilibrium point has a specific domain of stability. Stability regions could be overlapped and a bistable equilibria could be found, which means the coexistence of two stable equilibrium points. Hence, the solution converges to one of them depending on the initial conditions.

Source
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0257975PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8509987PMC
October 2021

### Dynamical Analysis of a Multiscale Model of Hepatitis C Virus Infection Using a Transformed ODEs Model.

##### Authors:
Hesham A Elkaranshawy Hossam M Ezzat Nermeen N Ibrahim

Annu Int Conf IEEE Eng Med Biol Soc 2020 07;2020:2451-2454

A mathematically identical ordinary differential equations (ODEs) model was derived from a multiscale partial differential equations (PDEs) model of hepatitis c virus infection, which helps to overcome the limitations of the PDE model in clinical data analysis. We have discussed about basic properties of the system and found the basic reproduction number of the system. A condition for the local stability of the uninfected and the infected steady states is presented. The local stability analysis of the model shows that the system is asymptotically stable at the disease-free equilibrium point when the basic reproduction number is less than one. When the basic reproduction number is greater than one endemic equilibrium point exists, and the local stability analysis proves that this point is asymptotically stable. Numerical sensitivity analysis based on model parameters is performed and therefore the result describes the influence of each parameter on the basic reproduction number.