Abstract—Influenza is the serious disease caused by an influenza virus. This disease is spreading widely that difficult to control. Vaccination is a commonly method for protect disease. In this study, thus, SVEIR (susceptible-vaccinated-exposed-infectious-recovered) model is used to predict the number of infected and the duration of an outbreak when it occurs. Using next generation method, it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value. It is also shown that the disease will persist within the population if the coverage level of vaccination is below this critical value. These results are verified by numerical simulations.

Index Terms—SVEIR epidemic model, stability, disease free equilibrium point, basic reproductive number.

The authors are with the Department of Mathematics at King Mongkut’s University of Technology Thonburi, Bangkok, 10140 Thailand (e-mail: siwaphonkp@ gmail.com, settapat.chi@kmutt.ac.th).

 

Cite: Siwaphorn Kanchanarat and Settapat Chinviriyasit, "A Mathematical Study of an Influenza Model with Vaccination," International Journal of Applied Physics and Mathematics vol. 4, no. 1, pp. 22-26, 2014.