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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 investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio ℛ 0 is less than unity. Otherwise, the system admits at least one positive periodic solutions if ℛ 0 is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio ℛ 1 is less than unity. When ℛ 1 is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Generally, the infection process of most vector-borne diseases involves a latent period in both human hosts and vectors. With regards to other publications, Tian and Song have recently proposed an SIR-SI model to analyze the effects of the incubation period on a vector-borne disease with nonlinear transmission rate. But they were silent on the fact that the partially immune individuals are slightly infective to mosquitoes. So, by considering that the partially immune individuals remain slightly infective to mosquitoes, a similar work has been done in this paper for malaria global transmission dynamics following an SIRS-SI pattern. The basic reproduction ratio has been calculated using the next-generation matrix method. Furthermore, using the characteristic equations and inequality analytical techniques, conditions are given under which the system exhibits threshold behavior as follows: when R0 < 1, the disease-free equilibrium is globally asymptotically stable meaning that the disease will eventually die out; and the unique endemic equilibrium is globally asymptotically stable when R0 > 1 meaning that the disease will persist. Finally, some numerical simulations have been performed to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results. [ABSTRACT FROM AUTHOR]

This paper adds new empirical evidence to the recent literature about the ways countries develop strong productive capacities by analyzing the patterns of export diversification across different levels of manufacturing content. In addition to the measures commonly used to study diversification, such as the number of active export lines and measures of 'discoveries in exports', we propose two new filters based on the concept of revealed comparative advantage (RCA). We use trade data at the 4-digit level for 176 countries from 1992 until 2011, and we classify all the products into three manufacturing categories (unprocessed, semi processed and finished goods). Data confirms that growing countries continue to add new commodities to their exports basket until they reach around US$ 25,000 of GDP per capita. More interestingly, we found that for many countries expanding the spectrum of commodities exported with comparative advantage (RCA) actually contribute to boosting new productive capacities in manufacturing sectors. This finding is robust to different econometric models and different country groups. [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]

This work is an extension of a previous publication. An optimal control theory is applied to a model of malaria transmission dynamics to investigate the control strategies for eliminating malaria using time dependent controls. Four main efforts are considered including the treatment of infected humans, the individual protection, vectors control strategies such as killing adult anopheles and both aquatic stages and the implementation of an imperfect vaccine which has already been tried in certain areas. The characterization of the optimal control is carried out via the Pontryagin's Maximum Principle which shows the necessary conditions for controlling malaria. Numerical simulations of the model show that restricted and proper use of control measures might considerably decrease the size of mosquito population and the number of infected among the human population accordingly. [ABSTRACT FROM AUTHOR]