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On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage

Ngwa G.A., Teboh-Ewungkem M.I., Dumont Y., Ouifki R., Banasiak J.. 2019. Journal of Theoretical Biology : 21 p..

A modelling framework that describes the dynamics of populations of the female Anopheles sp mosquitoes is used to develop and analyse a deterministic ordinary differential equation model for dynamics and transmission of malaria amongst humans and varying mosquito populations. The framework includes a characterization of the gonotrophic cycle of the female mosquito. The epidemiological model also captures a novel feature whereby treated human's blood can become mosquitocidal to the questing mosquitoes upon the successful ingestion of the treated human's blood. Analysis of the disease free system, that is the model in the absence of infection in the human and mosquito populations, reveals the presence of a basic offspring number, whose size determines the existence and stability of a thriving mosquito population in the sense that when we have only the mosquito extinction steady state which is globally asymptotically stable, while for N?>?1 we have the persistent mosquito population steady state which is also globally asymptotically stable for these range of values of . In the presence of disease, still strongly affects the properties of the epidemiological model in the sense that for the only steady state for the system is the mosquito extinction steady state, which is globally and asymptotically stable. As increases beyond unity in the epidemiological model, we obtained the epidemiological basic reproduction number, R0. For R0?

Mots-clés : afrique; pacifique occidental; amérique tropicale; asie du sud-est; afrique au sud du sahara

Thématique : Méthodes mathématiques et statistiques; Autres thèmes; Ecologie animale

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