On a delayed epidemic model with non-instantaneous impulses

Liang Bai; Juan J. Nieto; José M. Uzal

doi:10.3934/cpaa.2020084

Article Contents

2020, Volume 19, Issue 4: 1915-1930. Doi: 10.3934/cpaa.2020084

This issue Previous Article Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary Next Article Longtime behavior for 3D Navier-Stokes equations with constant delays

On a delayed epidemic model with non-instantaneous impulses

1.
College of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
2.
Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain
3.
Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain

^*Corresponding author.
^*Corresponding author.

Dedicated to professor Tomás Caraballo on the occasion of his 60th birthday

Received: March 31, 2019

Revised: September 30, 2019

Published: January 2020

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Abstract

We introduce a non-instantaneous pulse vaccination model. Non-instantaneous impulsive nonlinear differential equations provide an adequate biomathematical model of some medical problems. In this paper we study some basic properties such as the attractiveness of the infection-free periodic solution and the permanence of some sub-population for a vaccine model where a constant fraction of the susceptible population is vaccinated in some periodic way. Our model is a system of nonlinear differential equations with impulses.

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Mathematics Subject Classification: Primary: 34A37, 92C60.

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Figure 1. Simulation with $ R^*<1 $, infection-free solution

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Figure 2. Simulation with $ R_*>1 $, permanence of infected population

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