Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis

Abstract

Abstract A deterministic model is developed to study the dynamics of poliomyelitis virus infection with vaccination in a population with insanitary conditions. The polio-free equilibrium is shown to be locally asymptotically stable whenever the basic reproduction number is less than one but global stability requires other conditions to be satisfied. The spread of the disease is also shown to be sensitive to the average contact rate with the faecal matter of the infectious individuals, the transmission probability, natural death rate and vaccination, probabilities of the exposed individuals progressing to the non-paralytic and paralytic classes, the open defecation parameter and the polio-induced death rate. Other interesting results are illustrated through numerical simulation of the model.