Modeling and analysis of an SI 1 I 2 R epidemic model with nonlinear incidence and general recovery functions of I 1

Thirthar A., Najji R., Bozkurt Yousef F., Yousef A.

Chaos Solitons & Fractals, vol.145, no.2021, pp.1-9, 2021 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 145 Issue: 2021
  • Publication Date: 2021
  • Journal Name: Chaos Solitons & Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Page Numbers: pp.1-9
  • Erciyes University Affiliated: Yes

Abstract

In this paper, we established a mathematical model of an SI 1 I 2 R epidemic disease with saturated inci- dence and general recovery functions of the first disease I 1 . Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stabil- ity is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we car- ried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct nu- merical simulations that supported our theoretical findings.