# American Institute of Mathematical Sciences

April  2020, 19(4): 1915-1930. doi: 10.3934/cpaa.2020084

## 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.

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

Received  April 2019 Revised  October 2019 Published  January 2020

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.

Citation: Liang Bai, Juan J. Nieto, José M. Uzal. On a delayed epidemic model with non-instantaneous impulses. Communications on Pure & Applied Analysis, 2020, 19 (4) : 1915-1930. doi: 10.3934/cpaa.2020084
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##### References:
Simulation with $R^*<1$, infection-free solution
Simulation with $R_*>1$, permanence of infected population