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ABSTRACT
Temperature has been shown to be a key environmental driver of Anopheles mosquito population dynamics since it affects processes such as parasite development, blood meal digestion, egg-production and even the aquatic stages of mosquitoes. Quite recently, insecticide resistance has reared its head and has been perceived to be a likely cause for control failure as resistance allows mosquitoes to survive exposure to insecticides doses that should have been lethal to them. Therefore, understanding the roles of these factors (temperature and insecticide resistance) is important in the fight against malaria. In this study, we present three non-autonomous mathematical models which provide mathematical and epidemiological insights to some challenging areas relating to the role of temperature and insecticide resistance on the population dynamics of malaria. These include; impact of indoor and outdoor temperature variations on the dynamics of malaria transmission, the impact of temperature on the efficacy of chemical-based controls and the resultant effects of insecticide resistance of malaria vectors on the dynamics of malaria transmission. The qualitative and quantitative properties of the models are rigorously analyzed using tools such as the next generation operator method, the center manifold theorem, the uniform persistence theorem, the comparison theorem, the Latin Hypercube Sampling as well as the partial rank correlation coefficient. Thresholds for malaria control and possible eradication are established. Local and global asymptotic stability results of equilibria are established. The models are analyzed for the existence of backward bifurcation phenomenon. Results from analysis of the models showed that the models will not undergo the phenomenon of backward bifurcation, whenever the associated reproduction number was less than unity; if disease induced mortality of infectious humans is absent. Thus, disease-free equilibrium was shown to be globally asymptotically stable whenever the corresponding reviii production number was less then unity, indicating that malaria cannot successfully invade the population. Further, the uniform persistence of the disease was established whenever the associated reproduction number was above unity. Uncertainty and sensitivity analysis of parameters of the models identified some key parameters that have significant influence on the dynamics of the models. Numerical simulations of the models showed the indoor and outdoor temperature variations, intensity of insecticide resistance and temperature effect on the efficacy of chemical based controls have significant impact on the transmission dynamics of malaria. Particularly, the results obtained in this work, shows that temperature of different micro habitats where mosquitoes rest plays a significant role in the transmission dynamics of malaria as where mosquitoes rest and how long they rest there will impact on the number of infectious mosquitoes in the population. Also, knowing theprevailing environmental temperature and the intensity of resistance present in a population is important as both impacts on the efficacy of public health control strategies like the use of insecticide treated nets.
