An Avian Influenza Mathematical Model


Supri bin Amir, Hideo Hirose


The 2nd BMIRC International Symposium on Frontiers in Computational Systems Biology and Bioengineering, January 29 - 30, 2013, Fukuoka, Japan.


Epidemiology is a study of the spread of a disease by looking at how it is distributed in the population and factors affecting the spread. Before an infectious disease becomes an epidemic, studies need to be carried out to understand how the spread occurs so that it can be contained.
Avian influenza is an infection caused by avian (bird) influenza (flu) A viruses. These influenza A viruses occur naturally among birds. Wild birds worldwide get flu A infections in their intestines, but usually do not get sick from flu infections. However, avian influenza is very contagious among birds and some of these viruses can make certain domesticated bird species, including chickens, ducks, and turkeys, very sick and kill them.
During an outbreak of avian influenza among poultry, there is a possible risk of infection for people who have contact with infected birds or surfaces that have been contaminated with secretions or excretions from infected birds. Studies have shown that direct contact with diseased poultry was the source of infection and found no evidence of person to person spread of the virus.
Mathematical modeling is a powerful tool that can be used to analyze and explain the spread of infectious. In the case of avian influenza, deterministic models were used for comparing interventions aimed at preventing and controlling influenza pandemics and stochastic models were proposed to model and predict the world wide spread of pandemic influenza.
In this paper, we present mathematical model deals with the dynamics of human infection by avian influenza both in birds and in humans. Stability analysis is carried out and the behavior of the disease is illustrated by simulation with different parameters values. This study also will be determined on qualitative analysis of the model of the spread of avian influenza to obtain the basic reproduction number is presented for a general compartmental disease transmission model base on a system of ordinary differential equations.

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