# Asymptotic behavior and semi-analytic solution of a novel compartmental biological model

## Authors

• Muhammad Sinan School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People's Republic of China
• Jinsong Leng School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People's Republic of China
• Misbah Anjum International School of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People's Republic of China
• Mudassar Fiaz Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

## Keywords:

local asymptotic stability, global asymptotic stability, Routh-Hurwitz criterion, COVID-19, infectious disease modeling

## Abstract

This study proposes a novel mathematical model of COVID-19 and its qualitative properties. Asymptotic behavior of the proposed model with local and global stability analysis is investigated by considering the Lyapunov function. The mentioned model is globally stable around the disease-endemic equilibrium point conditionally. For a better understanding of the disease propagation with vaccination in the population, we split the population into five compartments: susceptible, exposed, infected, vaccinated, and recovered based on the fundamental Kermack-McKendrick model. He's homotopy perturbation technique is used for the semi-analytical solution of the suggested model. For the sake of justification, we present the numerical simulation with graphical results.

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## Published

2022-06-24
CITATION METRICS
DOI: 10.53391/mmnsa.2022.008

## How to Cite

Sinan, M., Leng, J., Anjum, M., & Fiaz, M. (2022). Asymptotic behavior and semi-analytic solution of a novel compartmental biological model. Mathematical Modelling and Numerical Simulation With Applications, 2(2), 88–107. https://doi.org/10.53391/mmnsa.2022.008

## Section

Research Articles