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Modeling and Control of Malaria When Mosquitoes Are Used as Vaccinators

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  • Xue-Zhi Li
  • Sha-Sha Gao
  • Maia Martcheva

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.

Suggested Citation

  • Xue-Zhi Li & Sha-Sha Gao & Maia Martcheva, 2015. "Modeling and Control of Malaria When Mosquitoes Are Used as Vaccinators," Mathematical Population Studies, Taylor & Francis Journals, vol. 22(3), pages 145-171, September.
  • Handle: RePEc:taf:mpopst:v:22:y:2015:i:3:p:145-171
    DOI: 10.1080/08898480.2014.925322
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