Multi-Strain Epidemic Models of Mutating Viruses with Airborne Transmission Based on Cellular Automata and Ordinary Differential Equations

Abstract

The emergence of SARS-CoV-2 virus mutations is a pressing concern in the context of the COVID-19 pandemic. In this paper, a Susceptible–Infected–Recovered (SIR) compartmental model has been formulated in terms of cellular automata and ordinary differential equations to simulate the transmission dynamics of a virus. This model accounts for the potential of new virus mutations to create additional infections of a multi-strain disease while also considering the impact of vaccination on disease control within a population. The basic reproduction number of the disease is derived, and the effect of virus mutations and vaccination rates is evaluated on a population over five years. The results of numerical simulations demonstrate the significant role of maintaining high vaccination rates in controlling the spread of the virus, even when assuming that all variants have similar illness characteristics and that a single shot of vaccine provides complete and lifelong protection against all strains. The findings underscore the necessity for countries to implement a consistent and high-level vaccination plan as soon as vaccines become available in order to mitigate the impact of a pandemic effectively. In conclusion, this study highlights the importance of taking into account the potential impact of virus mutations for controlling the COVID-19 pandemic. Furthermore, it emphasizes the critical role of vaccination in limiting the spread of the virus, and emphasizes the need to implement and maintain high vaccination rates as part of a comprehensive approach to managing the ongoing pandemic.