Thesis Abstract

Abstract
Hepatitis B virus (HBV) infection is a major global health concern, with millions of people affected worldwide. One of the challenges in controlling the spread of HBV is the presence of an infectious latent period where individuals can unknowingly transmit the virus to others. In this study, we develop a mathematical model to simulate the spread of HBV with an infectious latent period. The model incorporates key parameters such as the transmission rate, recovery rate, and the duration of the infectious latent period. By using mathematical equations and computational simulations, we are able to track the dynamics of HBV transmission within a population over time. Our model also considers factors such as vaccination rates and the impact of public health interventions on reducing the spread of the virus. Through our simulations, we are able to analyze the effectiveness of different control strategies in curbing the spread of HBV. We investigate the role of early detection, treatment, and vaccination in reducing the overall burden of HBV in a population. Our results show that increasing vaccination coverage and improving access to testing and treatment can significantly reduce the number of new infections and prevent further transmission of the virus. Furthermore, we explore the impact of behavioral factors and social networks on the spread of HBV. By incorporating human behavior into our model, we are able to study how individual interactions and contact patterns influence the transmission dynamics of the virus. This allows us to evaluate the effectiveness of targeted interventions aimed at high-risk populations and communities. Overall, our study provides insights into the complex dynamics of HBV transmission and the potential strategies for controlling the spread of the disease. By combining mathematical modeling with computational simulations, we are able to simulate various scenarios and assess the impact of different interventions on the prevalence of HBV. Our findings can inform public health policies and guide decision-making to reduce the burden of HBV worldwide.

Thesis Overview

1.0 INTRODUCTION

1.1 BACKGROUND OF STUDY

The spread of the HBV in Nigeria has posed a lot of threat to health and well being citizens in Nigeria. It is evident that about a third of the world’s population, approximately 2 billion people gets infected with hepatitis B virus in their life time. About 360 million people remain chronically infected carriers of the disease, most of whom are unaware of their HBV status and about 20% – 30% of whom will eventually die from chronic sequel. The prevalence of HBV infection varies from country to country, depending upon a complex behavioral, environmental and host factors. Chronic HBV can lead to hepatocellular carcinoma after 20 years among persons with chronic HBV infection; the risk for premature death from cirrhosis or hepatocellular carcinoma is 15% – 25%.

Hepatitis B is a disease that is characterized by inflammation of the liver and is caused by infection by the hepatitis B virus. According to (WHO, 2002) stated that hepatitis may be caused by drugs or viral agents; these viral agents include the hepatitis A, B, C, D, E, F, G and H viruses. Hepatitis B is one of the world’s most serious health problems. More than a billion people around the world have serological indicators of past or present infection with hepatitis B virus (HBV).

According to (White and Fenner (1994), Platkov et al (2001), Carriapa et al (2004), Fernandez et al (2006), Onuzulike and Ogueri (2007)) in their research stated that Over 300 million people are chronic carriers of the virus. The fast spread of HBV shows that is very communicable.

It is evident according to (WHO, 2002) that HBV infection can be transmitted from mother to child (vertical), contact with an infected person (horizontal transmission), sexual contact (homosexual and heterosexual transmission) with infected partners, exposure to blood or other infected fluids and contact with HBV contaminated instruments

HBV control measures include vaccination, education, screening of blood and blood products; and treatment (CDC, 2005).

According to (Anderson and May, 1991) stated that epidemiological models help to capture infection or disease transmission mechanisms in a population in a mathematical frame-work in order to predict the behavior of the disease spread through the population.

1.2 STATEMENT OF PROBLEM

What really instigated the study was the massive spread of HBV in Nigeria and most of the African countries. Several efforts has been put in place by the federal government of Nigeria and world health organization (WHO) through the ministry of health in Nigeria to combat HBV.

Secondly mathematicians all over the world have come with up with several model to help solve the model and simulate the spread of HBV; there have been a lot of failed model.

1.3 AIMS AND OBJECTIVES OF STUDY

The main aim of the research work is evaluate the modeling and simulation of the spread of HBV with infectious latent. Other specific objectives of the study include:

1. To find the existence and uniqueness of the solution to the model

2. To carry out sensitivity analysis on Ro to ascertain which parameter that is most sensitive and that should be targeted by way of intervention.

3. To examine the local stability of the model equation using the modified implicit function theorem

1.4 RESEARCH QUESTION

The study came up with research questions so as to ascertain the above stated objectives. The research questions are stated below as follows:

1. How to find the existence and uniqueness of the solution to the model?

2. How to carry out sensitivity analysis on Ro to ascertain which parameter that is most sensitive and that should be targeted by way of intervention?

3. How to perform the local stability of the model equation using the modified implicit function theorem?

1.5 SIGNIFICANT OF STUDY

The study on modeling and simulating of the spread of HBV disease with infectious latent will be of immense benefit to the ministry of health of Nigeria, the World health organization (WHO) and other researchers that wishes to carryout similar research on the above topic as it will discuss the local stability of the model equation using the modified implicit function theorem and also sensitivity analysis on Ro to ascertain which parameter that is most sensitive and that should be targeted by way of intervention

1.6 SCOPE OF STUDY

The study on modeling and simulation of the spread of HBV disease with infectious latent will cover the areas of local stability of the model equation and implicit function theorem

1.7 DEFINITION OF TERMS

HBV: Hepatitis B virus is a viral infection that attacks the liver and can cause both acute and chronic disease. The virus is transmitted through contact with the blood or other body fluids of an infected person.