Modeling and Control of Malaria When Mosquitoes Are Used as Vaccinators

Xue-Zhi Li, Sha-Sha Gao and Maia Martcheva

Mathematical Population Studies, 2015, vol. 22, issue 3, 145-171

Abstract: From the idea of turning mosquitoes into vaccinators, a first model of the transmission of malaria based on standard incidence leads to express the basic reproduction number R 0 (ψ) and the effective reproduction number ℛ(ψ) as a function of the vaccination rate ψ. The disease-free equilibrium is locally asymptotically stable if R 0 (ψ) > 1. A necessary and sufficient condition for backward bifurcation is derived. A unique endemic equilibrium exists if R 0 (ψ) > 1. A second model, based on mass action incidence, leads to express the basic reproduction number . The disease-free equilibrium is both locally asymptotically stable and globally stable if . A unique endemic equilibrium exists if and is locally asymptotically stable.

Date: 2015
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DOI: 10.1080/08898480.2014.925322

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