On the dynamics of a system modeling waterborne disease

Abstract Infectious diseases continue to debilitate and to cause death world- wide. Several different factors must be considered in attempting to understand waterborne disease dynamics, including different transmission pathways. A limitation of current modeling studies in waterborne diseases, however, is that the intrinsic dynamics of the pathogens are poorly addressed, leading to in- complete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. In this paper, we formulate an ordinary differential equations model with bacterial growth with Allee effect and adopt an adequate functional response to express, significantly, the shape of direct transmission. The existence of biologically meaningful equilibria and their stability is investigated. Numerical simulations of the obtained results applied to concrete cases are shown.