Modeling the effects of lethal and non-lethal predation on the dynamics of tick-borne disease

Tick-borne illnesses are transmitted to mammals like rodents and deer by infected ticks. These illnesses have shown dramatic increase in recent times, thereby increasing public health risk in the United States. Additionally, these mammals can be impacted by predation and the fear of their predators. In this study, we modeled the lethal and non-lethal effect of predation of the mammals on the dynamics of tick-borne disease using ehrlichiosis as our model disease system. Results of the theoretical analysis of reduced form of the model indicate that the model equilibria are stable when the tick fecundity and mortality rates are not host dependent. Furthermore, predator-induced fear and predator attack rates are two of the significant parameters of the model outputs from the sensitivity analysis carried out. Numerical simulation of the model shows that the combined impact of both lethal and non-lethal predation sets off a cascading chain reaction leading to a corresponding reduction in the prey and tick populations; in particular there are more infected larvae when infected prey population are low and few infected larvae when there are more infected prey. Similar dynamics was observed for the infected nymphs and adult ticks and infected predator population. Furthermore as the fear of the predator increases, the prey population reduces which subsequently lead to a decrease in the tick populations and subsequently disease in the community.