Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune

Siyu Liu; Mingwang Shen; Yingjie Bi; Siyu Liu; Mingwang Shen; Yingjie Bi

doi:10.3934/mbe.2020203

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3601-3617. doi: 10.3934/mbe.2020203

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Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune

1.
School of Public Health, Jilin University, Changchun, Jilin, 130021, China
2.
China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, 710061, China
3.
School of Mathematics, Jilin University, Changchun, Jilin, 130012, China

Received: 17 March 2020 Accepted: 09 May 2020 Published: 13 May 2020

Vaccination strategy is considered as the most cost-effective intervention measure for controlling diseases. It will strengthen the immunity and reduce the risks of infections. In this paper, a new delayed epidemic model with interim-immune and mixed vaccination strategy is studied. The diseasefree periodic solution is obtained by twice stroboscopic mapping and the corresponding dynamical behavior is analyzed. We determine a threshold parameter R₁, the disease-free periodic solution is proved to be global attractive if R₁ < 1. We also establish a threshold parameter R₂ for the permanence of the model, i.e., if R₂ > 1, the infectious disease will exist persistently. Then, we provide numerical simulations to illustrate our theoretical results intuitively. In particular, a practical application for newtype TB vaccine under mixed vaccination strategy is presented, based on the proposed theory and the data reported by NBSC. The mixed vaccination strategy can achieve the End TB goal formulated by WHO in limited time. Our study will help public health agency to design mixed control strategy which can reduce the burden of infectious diseases.
- epidemic model,
- global attractivity,
- mixed vaccination strategy,
- delay,
- interim-immune
Citation: Siyu Liu, Mingwang Shen, Yingjie Bi. Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3601-3617. doi: 10.3934/mbe.2020203

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Abstract

Vaccination strategy is considered as the most cost-effective intervention measure for controlling diseases. It will strengthen the immunity and reduce the risks of infections. In this paper, a new delayed epidemic model with interim-immune and mixed vaccination strategy is studied. The diseasefree periodic solution is obtained by twice stroboscopic mapping and the corresponding dynamical behavior is analyzed. We determine a threshold parameter R₁, the disease-free periodic solution is proved to be global attractive if R₁ < 1. We also establish a threshold parameter R₂ for the permanence of the model, i.e., if R₂ > 1, the infectious disease will exist persistently. Then, we provide numerical simulations to illustrate our theoretical results intuitively. In particular, a practical application for newtype TB vaccine under mixed vaccination strategy is presented, based on the proposed theory and the data reported by NBSC. The mixed vaccination strategy can achieve the End TB goal formulated by WHO in limited time. Our study will help public health agency to design mixed control strategy which can reduce the burden of infectious diseases.

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