Dynamical analysis of novel COVID-19 epidemic model with non-monotonic incidence function

Abstract

In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID-19 in India. The proposed ${\mathrm{SI}}_u{I}_{k}R$ model is a modified version of the existing $\mathrm{SIR}$ model. Our model divides the infected class $I$ of $\mathrm{SIR}$ model into two classes: $I_u$ (unknown infected class) and $I_k$ (known infected class). In addition, we consider $R$ a recovered and reserved class, where susceptible people can hide them due to fear of the COVID-19 infection. Furthermore, a non-monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease-free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long-run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.

Keywords: basic reproduction number; epidemiological model; local and global stability; novel coronavirus; persistence.