An SIR Model to Study the Effects of Ecological Factors on the Spread of Carrier Dependent Infectious Diseases

Abstract

In this paper, an SIR model to study the spread of carrier dependent infectious diseases in a population with constant immigration is proposed and analyzed by considering ecological effects. It is assumed that the density of carrier population is governed by a generalized logistic model, the growth rate of which increases as the cumulative density of ecological factors increases. The cumulative density of ecological factors is also assumed to be governed by the population density dependent logistic model. The model is analyzed by using qualitative theory of differential equations and by computer simulation. It is shown that as the density of the carrier population, caused by ecological factors increases, the infectious disease spreads faster and it becomes more endemic. The growth of human population due to immigration further enhances the spread of infectious diseases.