Multi-host multi-patch mathematical epidemic models for disease emergence with applications to hantavirus in wild rodents

Most zoonotic pathogens are capable of infecting multiple hosts. These animal hosts can often move through a large territory and many different landscapes. In this investigation, we formulate and analyze multi-host and multi-patch mathematical models for disease emergence. In particular, we examine SIS and SIR epidemic models. We determine under what conditions the disease can emerge. In the multi-host models, we examine a single pathogen that can infect n different hosts. In the multi-patch models, a single host moves through n different patches. For the multi-host models, it is shown that the basic reproduction number increases with the number of hosts. Therefore, the possibility for disease emergence increases with the number of infected hosts. In the multi-patch models, the basic reproduction number for the system lies between the basic reproduction numbers for each disconnected patch. Therefore, connection of patches may or may not lead to disease emergence. It is shown that as the mobility of hosts between patches increases, the basic reproduction number approaches a limiting value. We also examine a three-patch model which supports two hosts. The basic reproduction number is found for this model. For each type of model, we also formulate a set of stochastic differential equations. These stochastic models introduce variability through the demographic changes. Numerical examples illustrate the dynamics of each of the models. The models have applications to Hantavirus in wild rodents as well as other zoonotic diseases with multiple hosts.