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[A mathematical model for malaria transmission dynamics involving variable mosquito populations is developed and analysed. The model, which comprises a system of nonlinear deterministic ordinary differential equations, takes into consideration the vital and realistic life style characteristics of the Anopheles sp mosquito’s reproductive life by explicitly counting the gonotrophic cycles that each female mosquito must complete during its reproductive life. One by-product of the gonotrophic cycle count is the implicit embedding of the incubation period of the disease within the mosquito population in the modelling framework. The underlying assumption in deriving the equations for the model is that the female Anopheles sp mosquito has a human biting habit. The general model is analysed and measurable indices linked to invasion, mosquito population persistence and extinction such as the basic offspring number are identified and computed. The model’s infection-free, or disease-free, state is a system of equations representing a demographic model for mosquito population growth which exhibits more dynamic variability including the possibility of a thriving mosquito population or that of mosquito extinction depending on the size of the basic offspring number. Also, measurable indices linked to the malaria disease transmissibility potential such as the basic reproduction number and the existence of an endemic equilibrium are also identified and computed. The results of the analysis show the dependence of the size of the reproduction number and size of endemic equilibrium on the size of the basic offspring number, as well as the number of gonotrophic cycles that each adult vector can complete in its entire reproductive life. Standard results from dynamical systems’ theory are used to establish global stability results for the disease-free equilibria.]
Published: Aug 6, 2020
Keywords: Reproductive gains; Gonotrophic cycle; Offspring number; Global stability; Mosquito–human–malaria interactive framework
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