Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (3): 47-55.doi: 10.3969/j.issn.1000-5641.2021.03.006

• Mathematics • Previous Articles     Next Articles

Analysis of vector-borne infectious disease model with age-structured and horizontal transmission

Shuangshuang LIANG(), Linfei NIE*(), Lin HU   

  1. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
  • Received:2020-01-19 Online:2021-05-25 Published:2021-05-26
  • Contact: Linfei NIE;


Considering the prevalence of variations in virus strains and the age of infection, a vector-borne infectious disease model with latent age and horizontal transmission is proposed. An exact expression for the basic reproduction number, ${\cal R} _0 $ , is given, which characterizes the existence of the disease-free equilibrium and the endemic equilibrium for this model. Next, by using a combination of linear approximation methods, constructing suitable Lyapunov functions, LaSalle invariance principles, and other methods, we prove that if ${\cal R}_0 <1 $ , then the disease-free equilibrium has global asymptotic stability, and the disease will eventually become extinct; if ${\cal R}_0>1$ , then the endemic equilibrium is globally asymptotically stable, and the disease will continue to form an endemic disease.

Key words: vector-borne infectious disease model, age-structured and horizontal transmission, the basic reproduction number, disease-free and endemic equilibrium, stability and persistence

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