Mathematical Models for the Spread and Control of Multi-strain Influenza-A Viruses in Indonesia

Author: Wuryatmo Sidik

Sidik, Wuryatmo, 2015 Mathematical Models for the Spread and Control of Multi-strain Influenza-A Viruses in Indonesia, Flinders University, School of Computer Science, Engineering and Mathematics

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Abstract

Indonesia has the highest number outbreaks of avian flu in poultry and the greatest number of human casualties due to avian flu. It has also been speculated that the country poses the biggest threat for a future epidemic caused by a mutated virus resulting from recombination between avian flu and other strains of influenza-A. Work to mitigate the impact of avian flu and control the spread of disease in Indonesia, where millions of poor people rely on poultry for their livelihoods, is very important. A synthesis of available best practice in emergency response is needed to advise the country in capacity building, surveillance methods, and approaches for coping with new introductions of avian flu as well as future emerging disease threats. Several important issues in the control and impact of avian flu in Indonesia are little understood. Indonesia has difficulties in containing avian flu due to enormous and complex problems. Four main non medical factors in the spread and control of the disease are domestic farming practices, the prominence of wet markets, lack of government coordination on disease prevention, and economic constraints. This thesis addresses the problems of modeling the effects of these factors to the spread and control of avian flu and possible mutated viruses. It is assumed that a mutated virus, referred to here as mutant-avian flu, emerges as a result of a rare virus recombination between avian flu and swine flu. More specifically, it is assumed that avian flu, swine flu and mutant-avian flu are spreading among linked populations of poultry and humans. The populations are characterized by their disease states. The dynamics of the disease states are described as deterministic processes and modeled in the form of well defined disease dynamic problems (DDPs) and optimal disease control problems (ODCPs). The basic reproduction numbers are defined for avian flu transmission among birds, swine flu transmission among humans and mutant-avian flu transmission among humans. The equilibrium points of the systems are given as functions of the basic reproduction numbers. Stability analysis of the equilibrium points are given. Some are globally asymptotically stable (GAS), and others are locally asymptotically stable (LAS). Disease controls are defined as functions of the basic reproduction numbers. The disease controls describe the effort to reduce the effectiveness of the force of infection. The models do not attempt to match observations in high detail but are intended to capture the main features of the disease dynamics under certain assumptions. As analytical tools, the models and methods developed in this study help to better understand the dynamic behavior of avian flu, swine flu and mutant-avian flu among linked populations of poultry and humans in Indonesia. The models presented in this thesis are intended to demonstrate the feasibility of constructing a model-based tool to inform decision making bodies in Indonesia regarding the management of future epidemics.

Keywords: mathematical epidemiology,disease dynamics,optiimal disease controls
Subject: Mathematics thesis

Thesis type: Doctor of Philosophy
Completed: 2015
School: School of Computer Science, Engineering and Mathematics
Supervisor: Assoc. Professor Murk Bottema