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Title: The Transmission Dynamics and Optimal Control of Hepatitis B in Ethiopia Using SVEIRS Model
???metadata.dc.contributor.*???: Prof. Okey Oseloka Oneyejekwe
Nurhasen, Hindia
Keywords: SVEIRS-Model;Mathematical Models;Vital Dynamics;Vaccinations;HB;HBV;Herd Immunity;Epidemiology Number;Optimal Control
Issue Date: Oct-2017
Publisher: Addis Ababa University
Abstract: An epidemic model is a simplified means of describing the transmission of communicable disease through individuals. In this paper the mathematics behind the model and the various tools for judging effectiveness of policies and control methods on the spread of infectious diseases in populations has been analyzed mathematically. And it has been applied to specific diseases to study the propagation of diseases using the mathematical epidemic model. Epidemic models are many types form that select SVEIRS model and discussed the dynamics and control of infectious diseases, but quantifying the underlying epidemic structure can be challenging especially for new and understudied diseases. SVEIRS model is that generalizes several classical deterministic epidemic models then apply it for Hepatitis B. Consider compartments of susceptible, vaccination, exposed, infected, and recovered humans without immunity and modeled the natural growth, natural death and death due to disease and the interactions between these populations. The model has two equilibrium states namely, the disease - free and the endemic equilibrium points. The stability of each equilibrium point discussed has been found to be stable or unstable. The basic reproduction number(R0) estimate the stability, with (R0 > 1) whenever the transmission rate was increased or the recovery rate reduced but turned to the disease die out with (R0 < 1) whenever the transmission rate was reduced or the recovery rate increased. The results of our sensitivity analysis showed that the most sensitive parameter that controls the spread of Hepatitis B is the initial infection rate of the susceptible, b and d or death rate. Decreasing the value of b at the same rate as the other parameter values completely decreases the proportions of both the infective and the exposed more effectively than any parameter value. Consider an optimal control problem subject to an SVEIRS Hepatitis B epidemic model with vaccination controls. Our aim is to find the best optimal control strategies to make the number of infectious individuals as small as possible and to keep the vaccination ratio of Hepatitis B as low as possible during a certain vaccination period that will minimize the cost of control. Pontryagin’s maximum principle to characterize the optimal levels of the controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal vaccination, drug and education using media differs according to the controlled and uncontrolled individuals and has a very desirable effect upon the population for reducing the number of infected individuals. The effect of vaccination on transmission dynamics of Hepatitis B is studied. The resulting optimality system also showed that, the use of vaccinating at the highest possible rate to the population as early as possible is essential for controlling an epidemic of the Hepatitis B disease. Finally model to simulate the data of Hepatitis B cases in the Ethiopia from 2015 and design a control strategy of the country to eliminate the epidemic for the future course with optimal control theory.
Description: Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Computational Sciences at Addis Ababa University
Appears in Collections:Thesis-Computational Science

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