Bio-Inspired Computational Methods for the Polio Virus Epidemic Model

In 2021, most of the developing countries are fighting polio, and parents are concerned with the disabling of their children. Poliovirus transmits from person to person, which can infect the spinal cord, and paralyzes the parts of the body within a matter of hours. According to the World Health Organization (WHO), 18 million currently healthy people could have been paralyzed by the virus during 1988–2020. Almost all countries but Pakistan, Afghanistan, and a few more have been declared polio-free. The mathematical modeling of poliovirus is studied in the population by categorizing it as susceptible individuals (S), exposed individuals (E), infected individuals (I), and recovered individuals (R). In this study, we study the fundamental properties such as positivity and boundedness of the model. We also rigorously study the model’s stability and equilibria with or without poliovirus. For numerical study, we design the Euler, Runge–Kutta, and nonstandard finite difference method. However, the standard techniques are time-dependent and fail to present the results for an extended period. The nonstandard finite difference method works well to study disease dynamics for a long time without any constraints. Finally, the results of different methods are compared to prove their effectiveness.