Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

Abstract

In this article, we investigate a diffusive two-strain epidemic model with non-monotone incidence rate and virus mutation. The positivity, existence and uniform boundedness of the solutions of the model system are studied. It is found that the system has three equilibrium points, namely the infection-free equilibrium point, the strain-2 endemic equilibrium point and both the strain-1 and strain-2 endemic equilibrium points. The global asymptotic stability analysis of the diffusive model system near all the equilibrium points is carried out by constructing appropriate Lyapunov functional. It is found that the system has no strain-1 endemic equilibrium point possibly due to the virus mutation. So, in this type of diseases, the infection due to strain-1 cannot be persistent in the community.

Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation

“…However, compared to investigations of the dynamical behaviors of multistrain epidemic models with vaccination and time delays, early studies have received little attention. The dynamics of a two-strain epidemic model were studied in ( Rajib Arefin et al., 2019 ; De León et al., 2022 ; M. et al., 2005 ; Meskaf et al., 2020 ; Farah et al., 2021 ; Li et al., 2022 ; Khyar & Allali, 2020 ; Li et al., 2010 ; Lazebnik & Bunimovich-Mendrazitsky, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang, Chen, & Liu, 2016 ; Theprungsimankul, Junsank, Abdulloh, & Chinviriyasit, 2011 ; Khatua, Pal, & Kar, 2014 ; Allali & Amine, 2022 ; Li, Zhang, & Zhou, 2020 ). Epidemic models with time delay were studied in ( Barro et al., 2018 ; Beretta & Breda, 2011 ; Dong et al., 2017 ; Farah et al., 2021 ; Ma et al., 2002 ; Nakata & Omori, 2015 ; Nastasi, Perrone, Taffara, & Vitanza, 2022 ; Yang et al., 2016 ; Yang & Zhang, 2012 ).…”

“…Multistrain models with vaccination behaviors were studied in ( Rajib Arefin et al., 2019 ; Zuo, Zhu, Meng, et al., 2022 ; De León et al., 2022 ; Zuo, Zhu, & Ling, 2022 ; M. et al., 2005 ; Yin et al., 2022 ; Han & Li, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang & Zhang, 2012 ). Stability analysis of multistrain models was found in ( Allali & Amine, 2022 ; Dong et al., 2017 ; Farah et al., 2021 ; Khatua et al., 2014 ; Khyar & Allali, 2020 ; Meskaf et al., 2020 ; Tchoumi & Tchuenche, 2021 ; Tiwari, Rai, Khajanchi, Gupta, & Misra, 2021 ; Yang & Zhang, 2012 ).…”

Qualitative analysis of a fractional-order two-strain epidemic model with vaccination and general non-monotonic incidence rate

“…Obviously, the classical bilinear incidence rate does not take into account the force effect due to control measures and social awareness when the number of infected becomes larger. For this reason, non-monotonic incidence rate functions have been widely investigated in the literature to describe these phenomena (see for instance [ 21 , 34 , 35 ]). In this paper, we consider a two-strain fractional-order SIR epidemic model with vaccination where an individual can be simultaneously infected with two strains of the same virus.…”