Mathematical modeling and analysis for controlling the spread of infectious diseases

Swati Tyagi; Subash C Martha; Syed Abbas; Amar Debbouche

doi:10.1016/j.chaos.2021.110707

Mathematical modeling and analysis for controlling the spread of infectious diseases

Chaos Solitons Fractals. 2021 Mar:144:110707. doi: 10.1016/j.chaos.2021.110707. Epub 2021 Feb 3.

Authors

Swati Tyagi^{1

2}, Subash C Martha², Syed Abbas³, Amar Debbouche⁴

Affiliations

¹ Department of Mathematics, Chandigarh University, Chandigarh-140413, India.
² Department of Mathematics, Indian Institute of Technology Ropar, Punjab-140001, India.
³ School of Basic Sciences, Indian Institute of Technology Mandi, H.P.-175005, India.
⁴ Department of Mathematics, Guelma University, Guelma 24000, Algeria.

Abstract

In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.

Keywords: 34D23; 35B32; 37B25; 93A30; 97M60; Basic reproduction number; Hopf Bifurcation; Infectious diseases; Lyapunov function; Mathematical model; Stability analysis; Time delay.