Modelling and Analysis of the Spread of Carrier Dependent Infectious Diseases: Effect of Cumulative Density of Infrastructure

Abstract

In this paper, a four dimensional SIS epidemic non-linear model with immigration is proposed and analyzed to study the effect of infrastructure on the spread of carrier dependent infectious diseases. It is assumed that the density of carrier population follows logistic model and its growth rate and carrying capacity increase with the cumulative density of infrastructures, which depends on population density non-linearly. The model has been analyzed by using stability
theory of differential equations and simulation. The model has three equilibria namely, disease free, carrier free and non-trivial endemic equilibrium. It is shown that the disease free and carrier free equilibria are always unstable and the endemic equilibrium, if exists, becomes locally as well as non-linearly stable under certain conditions. This analysis implies that as the cumulative density of infrastructures increases due to increase in human population density, not only the density of carriers increases but, the spread of carrier dependent infectious disease also increases. It is found that the disease becomes more endemic due to immigration. A numerical analysis of the model is also performed which supports the analytical results.