Effect of the epidemiological heterogeneity on the outbreak outcomes

Alina Macacu; Dominique J. Bicout; Alina Macacu; Dominique J. Bicout

doi:10.3934/mbe.2017041

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 735-754. doi: 10.3934/mbe.2017041

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Effect of the epidemiological heterogeneity on the outbreak outcomes

Alina Macacu ,
Dominique J. Bicout ^,

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

Received: 08 May 2016 Accepted: 15 October 2016 Published: 01 June 2017
MSC : Primary: 92D30; Secondary: 92D25, 37N25

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 $R_{0,i} \lt 1$. Whereas, when at least one of the individual $R_{0,i} \gt 1$, then the hosts "$i$" with $R_{0,i} \gt R_{0,j}$ undergo a dilution effect while the hosts "$j$" undergo an amplification effect.
- Host heterogeneity,
- avian influenza,
- compartmental model,
- wildfowl,
- multi-host pathogens
Citation: Alina Macacu, Dominique J. Bicout. Effect of the epidemiological heterogeneity on the outbreak outcomes[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 735-754. doi: 10.3934/mbe.2017041

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Abstract

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 $R_{0,i} \lt 1$. Whereas, when at least one of the individual $R_{0,i} \gt 1$, then the hosts "$i$" with $R_{0,i} \gt R_{0,j}$ undergo a dilution effect while the hosts "$j$" undergo an amplification effect.

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