Master of Science

Avian influenza has been causing infections and deaths among humans in different parts of the world in recent years. As of January 2014, the avian influenza disease of the H5N1 viral strain has caused 386 deaths out of 650 reported cases in world, signifying a high disease fatality rate of about 59.4%. In addition to its threat to human life, the spread of avian influenza can also affect other aspects of human life. In 2006, the World Bank reported that low and middle income countries, as defined by the World Bank, may lose up to 0.4% of their Gross Domestic Product (GDP) due to the culling of avians. In order to minimise the negative effects of avian influenza, a variety of intervention and prevention strategies are developed to control the spread of avian influenza. However, there are many limitations in implementing these strategies. Mathematical modelling can be used by government agencies and public health organisations to better understand the spread of avian influenza and effectiveness of the implemented strategies.

The proposed model in this study incorporated features of the SIR model for both human and avian population, and the intervention strategy of the culling of avians. Data from Indonesia was applied to this study since she had the highest number of incidences and fatalities of humans with avian influenza in the world as of 2013.

The proposed model was formulated using a non-linear system of seven ordinary differential equations, whose analytic or exact solution could not be easily obtained. A numerical solution was therefore employed to find an approximate solution to this system. More specifically, in this study, the Runge-Kutta method of Order 4 was used. Initial values were chosen with the aid of available data. Parameter values were estimated from published works before being refined by calibrating the model values to the data using non-linear least squares curve-fitting.

The model was well-validated for a preliminary study using a timeframe of 243 days. However, the model presented a significant over-estimate when the study was extended to a data set involving a timeframe of 2435 days. In reality, there were no reports of avian influenza of the H5N1 viral strain in Indonesia having a drastic change in virulence over this period. However, the culling of avians may have varied considerably since it is dependent on human intervention. Hence, the model is refined by incorporating a variable culling coefficient while assuming that the other parameters values remain constant.

By calibrating model values to available data, a set of discrete values for the culling coefficients that changed every four to seven days were obtained in the refined model. However, this may not be representative of the real-world phenomenon of culling since culling measures are unlikely to be changed so frequently. An analysis was done to obtain an average constant culling coefficient for a certain duration of months. The average culling coefficient values applied were appropriate and the resulting model provided a good fit of model results to data. Discussions and implications to public health are presented with reference to model results and simulations.