Modeling and analysis of an SI1I2R epidemic model with nonlinear incidence and general recovery functions of I1. (April 2021)

• Record Type: Journal Article
• Authors: Thirthar, Ashraf Adnan; Naji, Raid Kamel; Bozkurt, Fatma; Yousef, Ali
• Is Part Of: Chaos, solitons and fractals. Volume 145(2021)
• Publication Date: 2021-04
• Subjects: Epidemiology -- Local stability -- Global stability -- Local bifurcation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110746
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, we established a mathematical model of an S I 1 I 2 R epidemic disease with saturated incidence 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 stability 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 carried 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 numerical simulations that supported our theoretical findings.