Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks

Rundong Zhao; Qiming Liu; Huazong Zhang; Rundong Zhao; Qiming Liu; Huazong Zhang

doi:10.3934/mbe.2021154

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3073-3091. doi: 10.3934/mbe.2021154

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Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks

Department of Science and Culture, Shijiazhuang Branch, Army Engineering University of PLA, Shijiazhuang 050003, China

Received: 12 January 2021 Accepted: 22 March 2021 Published: 02 April 2021

In order to study the impact of the incubation periods of humans and vectors on diseases transmission, a novel vector-borne diseases model with two time delays on bipartite networks is proposed. The formula of the basic reproduction number $ R_0 $ is given, which is dependent on time delays. Moreover, the globally asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing appropriate Lyapunov functions. Finally, numerical simulations are carried out to verify the analysis results and reveal the influence of the structure of bipartite networks on the basic reproduction number.
- vector-borne diseases,
- bipartite networks,
- dynamical model,
- time delay,
- stability
Citation: Rundong Zhao, Qiming Liu, Huazong Zhang. Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3073-3091. doi: 10.3934/mbe.2021154

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Abstract

In order to study the impact of the incubation periods of humans and vectors on diseases transmission, a novel vector-borne diseases model with two time delays on bipartite networks is proposed. The formula of the basic reproduction number $ R_0 $ is given, which is dependent on time delays. Moreover, the globally asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing appropriate Lyapunov functions. Finally, numerical simulations are carried out to verify the analysis results and reveal the influence of the structure of bipartite networks on the basic reproduction number.

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