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In this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the model have been derived: the vector reproduction ratio ℛv and the basic reproduction ratio ℛ0. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on these two parameters. More precisely, we show that if ℛv is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛv is greater than one and ℛ0 is greater than one, the disease remains persistent and the system admits at least one positive periodic solution. Finally, using the reported monthly mean temperature for Burkina Faso, numerical simulations are carried out to illustrate our mathematical results.

In this paper, we present a mathematical model of malaria transmission dynamics with age structure for the vector population and a periodic biting rate of female anopheles mosquitoes. The human population is divided into two major categories: the most vulnerable called non-immune and the least vulnerable called semi-immune. By applying the theory of uniform persistence and the Floquet theory with comparison principle, we analyse the stability of the disease-free equilibrium and the behaviour of the model when the basic reproduction ratio $ \mathcal {R}_0 $ is greater than one or less than one. At last, numerical simulations are carried out to illustrate our mathematical results.

In this article, we propose three mathematical models of mosquito dynamics. The first model describes the dynamics of wild mosquitoes in combination with mechanical control and larvicide. For this model, we derive a threshold parameter $ \mathcal {N} $ N , called the basic number of offspring, and show that the trivial equilibrium is globally asymptotically stable when $ \mathcal {N}\leq ~1 $ N ≤ 1 , while if $ \mathcal {N} \gt 1 $ N > 1 , the non-trivial equilibrium is globally asymptotically stable. In the second model, we evaluated a constant release of Wolbachia-infected males in the wild mosquito population. Our analysis identified a critical threshold for releasing Wolbachia-infected male mosquitoes $ M_{i}^{\rm crit} $ M i crit to reduce or eliminate the wild mosquito population. In the third model, we assessed wild mosquito dynamics by periodically releasing Wolbachia-infected male mosquitoes. The analysis of this model produced two thresholds, $ T^{*} $ T ∗ the threshold on the release period and $ \Lambda ^{*} $ Λ ∗ the threshold on the release quantity. The existence of trivial periodic solutions is obtained, and the corresponding local and global stability conditions are proved by Floquet's theory and Lyapunov's stability theorem, respectively. We also prove the existence conditions for non-trivial periodic solutions and their local stability. Finally, we perform some numerical simulations to illustrate our theoretically pertinent results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a mathematical model of malaria transmission dynamics with maturation delay of a vector population in a periodic environment. The incidence rate between vector and human hosts is modeled by a general nonlinear incidence function which satisfies a set of conditions. Thus, the model is formulated as a system of retarded functional differential equations. Furthermore, through dynamical systems theory, we rigorously analyze the global behavior of the model. Therefore, we prove that the basic reproduction number of the model denoted by % is the threshold between the uniform persistence and the extinction of malaria virus transmission. More precisely, we show that if % is less than unity, then the disease-free periodic solution is globally asymptotically stable. Otherwise, the system exhibits at least one positive periodic solution if % is greater than unity. Finally, we perform some numerical simulations to illustrate our mathematical results and to analyze the impact of the delay on the disease transmission. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a mathematical model of malaria transmission dynamics with impulsive and periodic release of Wolbachia-infected male mosquitoes. Our objective is to evaluate the impact of periodic release of Wolbachia-infected male mosquitoes on malaria transmission. Subsequently, to find out how often and in what quantities Wolbachia-infected male mosquitoes need to be released to effectively reduce malaria transmission. By using the comparison principle, Floquet theory and some of the analytical methods, we obtain the basic reproduction number. Then, we demonstrated that the disease-free periodic solution is globally stable if the reproduction number is less than unity, and we prove the uniform persistence of the disease if the reproduction number is greater than unity. Finally, we perform numerical simulations to illustrate our theoretically pertinent results. [ABSTRACT FROM AUTHOR]