Puntani  Pongsumpun, Jiraporn  Lamwong, 
    Mathematical Model of Avian Influenza When there is the
Traveling of Tourists from the Risk Countries,
    International Journal of Soft Computing,
    Volume 11,Issue 3,
    2016,
    Pages 120-126,
    ISSN 1816-9503,
    ijscomp.2016.120.126,
    (https://makhillpublications.co/view-article.php?doi=ijscomp.2016.120.126)
    Abstract: Avian influenza is caused by influenza virus type A. First infected case was reported in Hong Kong during a poultry outbreak in 1997. After that, there were the reports of the sporadic outbreak in all regions. In this study, we consider the transmission model of avian influenza when there is the traveling of tourists from the risk countries. We consider the dynamical changes of three population groups: Thai human, Hong Kong human and bird populations. The behaviors of the modified equations are obtained by using a standard dynamical modeling method. This method is used for analyzing the behaviors of solutions. The stability conditions for the disease free and endemic equilibrium states are determined. The threshold parameter is defined by R<sub>0</sub>. When R<sub>0</sub>&lt;1, the disease-free state is locally asymptotically stable. If R<sub>0</sub>&gt;1, the endemic  equilibrium state is locally asymptotically stable. The numerical solutions are shown for supporting the theoretical results.
    Keywords: stability;endemic;steady state;disease free steady state;Basis reproductive number