Effect of the epidemiological heterogeneity on the outbreak outcomes

Multi-host pathogens infect and are transmitted by different kinds of hosts and, therefore, the host heterogeneity may have a great impact on the outbreak outcome of the system. This paper deals with the following problem: consider the system of interacting and mixed populations of hosts epidemiologically different, what would be the outbreak outcome for each host population composing the system as a result of mixing in comparison to the situation with zero mixing? To address this issue we have characterized the epidemic response function for a single-host population and defined a heterogeneity index measuring how host systems are epidemiologically different in terms of generation time, basic reproduction number R0 and, therefore, epidemic response function. Based on the individual epidemiological characteristics of populations, with heterogeneities and mixing affinities, the response of subpopulations in a multi-host system is compared to that of a single-host system. The case of a two-host system, in which the infection transmission depends solely on the infection susceptibility of the receiver, is analyzed in detail. Three types of responses are observed: dilution, amplification or no effect, corresponding to lower, higher or equal attack rates, respectively, for a host population in an interacting multi-host system compared to the zero-mixing situation. We find that no effect is generally observed for zero heterogeneity. A dilution effect is always observed for all the host populations when their individual R0,i < 1. Whereas, when at least one of the individual R0,i > 1, then the hosts ''i'' with R0,i > R0,j undergo a dilution effect while the hosts ''j'' undergo an amplification effect.