Modelling and simulation of the spread of hbv disease with infectious latent

Project Abstract

Hepatitis B Virus (HBV) is a highly infectious disease that affects millions of people worldwide. In this study, we develop a mathematical model to simulate the spread of HBV with an infectious latent period. The model incorporates key factors such as the transmission rate, recovery rate, and the rate of progression from the latent to the infectious stage. By analyzing the model, we aim to understand the dynamics of HBV spread and evaluate potential control measures. Our model divides the population into compartments representing susceptible individuals, latently infected individuals, infectious individuals, and recovered individuals. We use a system of differential equations to describe the flow of individuals between these compartments over time. The model parameters are based on epidemiological data and biological knowledge of HBV transmission and progression. Simulations of the model show that the spread of HBV with an infectious latent period can lead to different epidemic patterns compared to models without latency. The presence of an infectious latent period can result in prolonged outbreaks and higher peak prevalence. Sensitivity analysis of the model parameters highlights the importance of interventions targeting the transmission rate and the progression rate from the latent to the infectious stage. We further investigate the impact of control measures such as vaccination, treatment, and behavior change on the spread of HBV. Our results show that increasing vaccination coverage and early detection of infections can significantly reduce the burden of HBV in the population. We also find that targeted interventions, such as screening high-risk groups and promoting safe injection practices, can be effective in controlling the spread of the disease. Overall, our study provides insights into the complex dynamics of HBV transmission with an infectious latent period. The model serves as a valuable tool for policymakers and public health officials to design effective strategies for preventing and controlling HBV outbreaks. Future research can build upon this work by incorporating additional complexities, such as population heterogeneity and spatial dynamics, to enhance the realism of the model and improve its predictive power.

Project Overview

<p> </p><p><strong>1.0 INTRODUCTION</strong></p><p><strong>1.1 BACKGROUND OF STUDY</strong></p><p>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%.</p><p>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).</p><p>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.</p><p>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</p><p>HBV control measures include vaccination, education, screening of blood and blood products; and treatment (CDC, 2005).</p><p>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.</p><p><strong>1.2 STATEMENT OF PROBLEM</strong></p><p>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.</p><p>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.</p><p><strong>1.3 AIMS AND OBJECTIVES OF STUDY</strong></p><p>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:</p><p>1. To find the existence and uniqueness of the solution to the model</p><p>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.</p><p>3. To examine the local stability of the model equation using the modified implicit function theorem</p><p><strong>1.4 RESEARCH QUESTION</strong></p><p>The study came up with research questions so as to ascertain the above stated objectives. The research questions are stated below as follows:</p><p>1. How to find the existence and uniqueness of the solution to the model?</p><p>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?</p><p>3. How to perform the local stability of the model equation using the modified implicit function theorem?</p><p><strong>1.5 SIGNIFICANT OF STUDY</strong></p><p>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</p><p><strong>1.6 SCOPE OF STUDY</strong></p><p>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</p><p><strong>1.7 DEFINITION OF TERMS</strong></p><p><strong>HBV</strong>: 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.</p> <br><p></p>