Epidemiological Model of Influenza A (H1N1) Transmission in Ashanti Region of Ghana

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The pandemic potential of influenza A (H1N1) has required decision makers to act in the face of uncertainties. In this thesis we develop a deterministic Susceptible – Exposed – Infectious – Recovered (SEIR) model to study the spread of H1N1 using data from the Ashanti region of Ghana. The study is based on the assumption that the population is constant with birth rate equals death rate. It is also assumed that the population interacts freely (homogeneous mixing). The model has two equilibrium states. The stability of each equilibrium point namely, the disease – free and the endemic equilibrium points are discussed. The basic reproduction number (R_O) was estimated to be 1.0064 and was found to persist with〖 R〗_O>1 whenever the transmission rate was increased or the recovery rate reduced but turned to〖 R〗_O<1, whenever the transmission rate was reduced or the recovery rate increased. A simulation was run for five months and extended to sixteen months in the neighbourhoods of the disease – free and endemic states and showed that near the disease – free state, the proportion of infectives had no effect on the susceptible population. However, as the number of infectives was increased in the neighborhood of the endemic equilibrium point, the susceptible population declined gradually reaching a minimum value at the last month. The recovered proportion of the population on the other hand, increased exponentially with time reaching a maximum value at the last month of the simulation. It is concluded that rapid vaccination is the most important factor to control the spread of H1N1 in case of an outbreak and that 0.64% of the susceptible population needs to be vaccinated in order to bring the disease under control.  
A thesis submitted to the Department of Mathematics In partial fulfillment of the requirement for the award of the degree of Master of Philosophy in Mathematics College of Science