Analysis of a model for waterborne diseases with Allee effect on bacteria

A limitation of current modeling studies in waterborne diseases (one of the leading causes
of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading
to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on
disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs
model with bacterial growth inducing Allee effect. We adopt an adequate functional response to
significantly express the shape of indirect transmission. The existence and stability of biologically
meaningful equilibria is investigated through a detailed discussion of both backward and Hopf
bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical
simulations confirming the obtained results in two different scenarios are shown.