Nur Asiyah, Basuki Widodo, Suhud Wahyudi, Suhud Wahyudi : Speading Dynamic of a Contagious in Heterogenic Population of Living beings with MultiGroup Model aproach
Prof. Dr. Basuki Widodo M.Sc.
INTERNATIONAL CONFERENSI ON MATHEMATICS, STATISTICS, AND FINANCIAL MATHEMATICS 2014 (ICMSFM2014)
Stability Analysis, Liapunov Function, Nonlinear infection rate, Network
Abstract: A heterogeneous ecosystem can be divided to many groups of homogenous. Therefore, if there is spreading of disease inside the ecosystem then the occurring of cross relation infection between those groups are able to be analyzed.
A mathematical model of a spreading contagious disease (epidemic) in a population of living beings, which are grouped as many of homogenous one, will be analyzed for the local and global stability from the system critical point with a multi group model approach. This paper provides a case of two groups where its infection rate is nonlinear. The method used here is to utilize Routh-Hurwitz criteria to analyze its local stability and the construction of Liapunov function for its global stability by implementing vector graph. By using graph theory approach, the system can be drawn as a network where each vertex represents a homogenous group and an edge (j,i)which is present if and only if the disease can be contagious from group i to group j.
After knowing the system critical point stability type of this nonlinear infection rate multi group epidemic model, then the number of reproduction ROcan be found to understand whether this epidemic disease will be extinguished later or becoming endemic instead.
Keywords:Stability Analysis, Liapunov Function, Nonlinear infection rate, Network