State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate-Reference-Cited by-同舟云学术

State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate

Published:2019-02-06 Issue: Volume:2019 Page:1-10
ISSN:1748-670X
Container-title:Computational and Mathematical Methods in Medicine
language:en
Short-container-title:Computational and Mathematical Methods in Medicine

Author:

Liu Kaiyuan¹^ORCID,Zhang Tongqian²³^ORCID,Chen Lansun⁴^ORCID

Affiliation:

1. College of Mathematics and Information Science, Anshan Normal University, Anshan 114016, China

2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

3. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Abstract

In this paper, the state-dependent pulse vaccination and therapeutic strategy are considered in the control of the disease. A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. Then for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a unique order-1 homoclinic cycle, and by choosing p as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when p changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Immunology and Microbiology,General Biochemistry, Genetics and Molecular Biology,Modelling and Simulation,General Medicine

Link

http://downloads.hindawi.com/journals/cmmm/2019/3859815.pdf

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