The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission

Authors:
Zhonghua Lu;Xuebin Chi;Lansun Chen
Affiliations:
Supercomputing Center of Computer Network Information Center Chinese Academy of Sciences, Beijing, 100080, P.R. China and Statistic Department, Xi'an Institute of Finance and Economics Xi'an, 7100 ...;Supercomputing Center of Computer Network Information Center Chinese Academy of Sciences, Beijing, 100080, P.R. China;Institute of Mathematics, Academy of Mathematics and System Sciences Beijing 100080, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

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Abstract

A SIR epidemic model with horizontal and vertical transmission is presented. The dynamics of this disease model under constant and pulse vaccination are analyzed. Theoretical results show that under constant vaccination, the dynamic behavior is similar to no vaccination. But under a planned pulse vaccination regime, the system converges to a stable periodic solution with the number of infectious individuals equal to zero. Further, the global stability of an infection-free periodic solution is analyzed. And the existence of a nontrivial periodic solution (endemic) is considered by using bifurcation theory. Our theoretical results are confirmed by numerical simulations. The effectiveness of constant and pulse vaccination policies are compared.