Modeling and Control of Malaria When Mosquitoes Are Used as Vaccinators

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.