Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination

Anqi Miao; Jian Zhang; Tongqian Zhang; B G Sampath Aruna Pradeep

doi:10.1155/2017/4820183

Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination

Comput Math Methods Med. 2017:2017:4820183. doi: 10.1155/2017/4820183. Epub 2017 Jul 6.

Authors

Anqi Miao¹, Jian Zhang¹, Tongqian Zhang^{1

2}, B G Sampath Aruna Pradeep³

Affiliations

¹ College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
² 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.
³ Department of Mathematics, University of Ruhuna, 81000 Matara, Sri Lanka.

Abstract

A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.

MeSH terms

Communicable Disease Control*
Computer Simulation
Disease Eradication / statistics & numerical data
Humans
Infectious Disease Transmission, Vertical / statistics & numerical data*
Models, Biological*
Stochastic Processes
Vaccination / statistics & numerical data*