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 epidemiolog...
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AIMS Press
2017-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017041 |
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| author | Alina Macacu Dominique J. Bicout |
| author_facet | Alina Macacu Dominique J. Bicout |
| author_sort | Alina Macacu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-01a895fb1f014629bc578647216ffe61 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-01a895fb1f014629bc578647216ffe612025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114373575410.3934/mbe.2017041Effect of the epidemiological heterogeneity on the outbreak outcomesAlina Macacu0Dominique J. Bicout1Biomathematics and Epidemiology, EPSP -TIMC, UMR 5525 CNRS, Grenoble Alpes University, VetAgro Sup Lyon, 1 avenue Bourgelat -69280 Marcy l'Etoile, FranceBiomathematics and Epidemiology, EPSP -TIMC, UMR 5525 CNRS, Grenoble Alpes University, VetAgro Sup Lyon, 1 avenue Bourgelat -69280 Marcy l'Etoile, FranceMulti-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.https://www.aimspress.com/article/doi/10.3934/mbe.2017041host heterogeneityavian influenzacompartmental modelwildfowlmulti-host pathogens |
| spellingShingle | Alina Macacu Dominique J. Bicout Effect of the epidemiological heterogeneity on the outbreak outcomes Mathematical Biosciences and Engineering host heterogeneity avian influenza compartmental model wildfowl multi-host pathogens |
| title | Effect of the epidemiological heterogeneity on the outbreak outcomes |
| title_full | Effect of the epidemiological heterogeneity on the outbreak outcomes |
| title_fullStr | Effect of the epidemiological heterogeneity on the outbreak outcomes |
| title_full_unstemmed | Effect of the epidemiological heterogeneity on the outbreak outcomes |
| title_short | Effect of the epidemiological heterogeneity on the outbreak outcomes |
| title_sort | effect of the epidemiological heterogeneity on the outbreak outcomes |
| topic | host heterogeneity avian influenza compartmental model wildfowl multi-host pathogens |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017041 |
| work_keys_str_mv | AT alinamacacu effectoftheepidemiologicalheterogeneityontheoutbreakoutcomes AT dominiquejbicout effectoftheepidemiologicalheterogeneityontheoutbreakoutcomes |