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. 2012 Apr 19;1(2):267–282. doi: 10.1007/s40065-012-0013-6

Analysis of an influenza A (H1N1) epidemic model with vaccination

Xueyong Zhou 1,2,✉, Zhen Guo 3
PMCID: PMC7149170  PMID: 38624337

Abstract

A nonlinear mathematical model for the spread of influenza A (H1N1) infectious diseases including the role of vaccination is proposed and analyzed. It is assumed that the susceptibles become infected by direct contact with infectives and exposed population. We take under consideration that only a susceptible person can be vaccinated and that the vaccine is not 100% efficient. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccination reproduction number Inline graphic which is, if less than one, the disease dies out provided the vaccine efficacy is high enough, and otherwise the infection is maintained in the population. It is also shown that the spread of an infectious disease increases as the infective rate increases.

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Mathematics Subject Classification (2010): 92B05, 34D05

Acknowledgments

We would like to thank the anonymous referees for their careful reading of the original manuscript and their many valuable comments and suggestions that greatly improved the presentation of this work. This work is supported by the National Natural Science Foundation of China (No. 11071011) and Natural Science Foundation of the Education Department of Henan Province (Nos. 2010A110017 and 2011B110028).

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