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Article Dans Une Revue Nonautonomous dynamical systems Année : 2022

Mathematical modeling of the dynamics of vector-borne diseases transmitted by mosquitoes : taking into account aquatic stages and gonotrophic cycle

Abou Bakari Diabaté
  • Fonction : Auteur
Boureima Sangaré
Ousmane Koutou

Résumé

In this paper, we formulate a mathematical model of vector-borne disease dynamics. The model is constructed by considering two models : a baseline model of vector population dynamics due to Lutambi et al. that takes into account the development of the aquatic stages and the female mosquitoes gonotrophic cycle and an SI-SIR model describing the interaction between mosquitoes and human hosts. We brie y study the baseline model of vectors dynamics and, for the transmission model, we explicitly compute the equilibrium points, and by using the method of Van den Driesshe and J. Watmough, we derive the basic reproduction number R. Otherwise, thanks to Lyapunov's principle, Routh-Hurwitz criteria and a favorable result due to Vidyasagar, we establish the local and global stability results of the equilibrium points. Furthermore, we establish an interesting relationship between the mosquito reproduction number Rv and the basic reproduction number R. It then follows that aquatic stages and behavior of adult mosquitoes have a signi cant impact on disease transmission dynamics. Finally, some numerical simulations are carried out to support the theoretical ndings of the study.
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Dates et versions

hal-04219238 , version 1 (27-09-2023)

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Abou Bakari Diabaté, Boureima Sangaré, Ousmane Koutou. Mathematical modeling of the dynamics of vector-borne diseases transmitted by mosquitoes : taking into account aquatic stages and gonotrophic cycle. Nonautonomous dynamical systems, 2022, 9, pp.205 - 236. ⟨10.1515/msds-2022-0155⟩. ⟨hal-04219238⟩

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