Epidemic dynamics of an infection through the pathogen density in the environment

Abstract

[EN] We propose a mathematical model for the indirect transmission via a contaminated environment by a disease agent and we analyze the possibility that the initial infection can spread in the population. We have used the significance of the basic reproduction number, since the disease free state is either stable or unstable depending on its value, to obtain an explicit expression for $ R_0$. This expression is found to give threshold conditions for the stability of the disease- free equilibrium or the existence of an endemic equilibrium in a population.