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Effect of the epidemiological heterogeneity on the outbreak outcomes

. Biomathematics and Epidemiology, EPSP -TIMC, UMR 5525 CNRS, Grenoble Alpes University, VetAgro Sup Lyon, 1 avenue Bourgelat -69280 Marcy l'Etoile, France

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 $R_0$ 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 $R_{0,i} <1 whereas="" when="" at="" least="" one="" of="" the="" individual="" r_="" 0="" i="">1$, then the hosts "$i$" with $R_{0,i}>R_{0,j}$ undergo a dilution effect while the hosts "$j$" undergo an amplification effect.

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Copyright Info: © 2017, Dominique J. Bicout, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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