Effect of pollution on dynamics of SIR model with treatment

Abstract

In this paper, an SIR epidemic model with treatment affected by pollution is proposed. The existence, local and global dynamics of the model are studied. It is shown that backward bifurcation occurs at R0 < 1 and p0 < 1 because of insufficient capacity of treatment. It is also found that due to pollution the number of infective has gone to a very high level. As a result, backward bifurcation occurs for R0 < 1, even when p0 > 1. Further, there exist bistable endemic equilibria for a very low capacity for R0 > 1. Thus, we found that disease can be eradicated for R0 < 1 only by increasing the capacity to a sufficiently high level. Persistence of endemicity of the system is obtained and the mathematical results suggest that the basic reproduction number is insufficient for disease eradication. Numerical simulations are presented to illustrate the results obtained.