Abstract
ABSTRACTIn this study, we first formulate a baseline discrete-time mathematical model for malaria transmission where the survival function of mosquitoes is of Beverton–Holt type. We then introduce sterile mosquitoes to the baseline model to explore the transmission dynamics with sterile mosquitoes. We derive formulas for the reproductive number of infection and determine the existence and uniqueness of endemic fixed points as well, for the models with or without sterile mosquitoes. We then study the impact of the releases of sterile mosquitoes on the disease transmissions by investigating the effects of varying the release rates of the sterile mosquitoes. We use a numerical example to illustrate our results for all cases and finally give brief discussions of our findings.
Highlights
Mosquito-borne diseases, such as malaria, are a big concern for the public health worldwide
We derived a formula for the reproductive number of infection R0 in (2.9) and showed that the infection-free fixed point of the baseline model is asymptotically stable if R0 < 1 and unstable if R0 > 1
We only consider the case of constant releases of sterile mosquitoes
Summary
Mosquito-borne diseases, such as malaria, are a big concern for the public health worldwide. There are many models in the literature for the study of vector-borne diseases and models incorporating sterile mosquitoes, are formulated for the disease transmission dynamics [1, 9, 17, 18, 20, 28]. As time steps are sufficiently small or population sizes are sufficiently large, these models are valid The results from those continuous-time models have shown their significance in helping understand the transmission dynamics and make useful strategies for control and prevention of the disease.
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