Mathematical Modeling of Polio Virus Infection Incorporating Immigration and Vaccination

Abstract

A deterministic mathematical model for polio infection dynamics with emphasis on immigration and vaccination was formulated and analyzed. We derived the basic reproduction number, of the model formulated. The effective reproduction number was computed using the next generation matrix to enable a qualitative analysis to be carried out on the model. Also, the disease-free equilibrium and endemic equilibrium points were computed. On analyzing the equilibrium points, we found that the disease-free equilibrium point is locally asymptotically stable if and the condition for existence on an Endemic Equilibrium point was also established. More so, numerical simulations showed that vaccination coverage of about 75% would be enough to eradicate polio from the population.