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Global Dynamics for a Vector-Borne Disease Model with Class-Age-Dependent Vaccination, Latency and General Incidence Rate

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Abstract

Considering the variability of vaccine efficacy and infection conversion rate, a mathematical model for vector-borne disease transmission by incorporating age of vaccination and infection is proposed, where, the latency of disease in the host population, general nonlinear incidence rate, and vaccination effectiveness are also formulated to analyze their effects for the spread of the vector-borne. The existence and local stability of steady states, the uniform persistence and asymptotic smoothness of this model are studied. Moreover, the exact expression of the basic reproduction number is derived. By applying the fluctuation lemma and the suitable Lyapunov functional, the global dynamics of steady states are investigated. That is, if the basic reproduction number is less than 1, the disease-free steady state is globally asymptomatically stable, and the disease dies out; if the basic reproduction number is greater than 1, the endemic steady state is globally asymptomatically stable, and the disease becomes endemic. Finally, numerical simulations are performed to explain the main theoretical results.

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Acknowledgements

We are grateful to the editors and the anonymous referees for their careful reading and helpful comments which led to great improvement of our paper. This research is partially supported by the National Natural Science Foundation of China (Grant Nos. 11961066 and 11771373), the Scientific Research Programmes of Colleges in Xinjiang (Grant No. XJEDU2018I001).

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  1. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Shengfu Wang & Lin-Fei Nie

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  1. Shengfu Wang
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Correspondence to Lin-Fei Nie.

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Wang, S., Nie, LF. Global Dynamics for a Vector-Borne Disease Model with Class-Age-Dependent Vaccination, Latency and General Incidence Rate. Qual. Theory Dyn. Syst. 19, 72 (2020). https://doi.org/10.1007/s12346-020-00407-z

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