The direct or indirect role of viruses and bacteria in spreading diseases in humans has been of critical importance in understanding their dynamics. However, not much attention has been paid toward the spread or control of diseases among animals caused by bacteria or viruses. Although the directly transmitted diseases in prey have been well explored in the literature, the indirectly transmitting diseases remain unexplored. In this study, we assume that the prey species become infected through ingestion of water from a reservoir contaminated by bacteria. We also investigate the dynamics of the related seasonally forced system, taking into account certain model parameters as functions of time. Both mathematical and numerical analyses are performed for autonomous and nonautonomous models. Sensitivity analysis indicates that the elevated rate of disease transmission and higher bacterial loads in the environmental reservoir substantially raise the infected prey population, which in turn poses an indirect risk to predator persistence. For the seasonally driven system, several dynamical features such as periodic solutions, higher periodic solutions, and bursting patterns are observed.
Roy et al. (Sat,) studied this question.