Modelling And Simulation Of The Spread Of Hbv Disease With Infectious Latent
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Modelling And Simulation Of The Spread Of Hbv Disease With Infectious Latent
Chapter one
1.0 Introduction
1.1 Background of Study
The rise of HBV in Nigeria has created significant threats to the health and well-being of Nigerian individuals. It is clear that around one-third of the world’s population, or approximately 2 billion people, will become infected with the hepatitis B virus during their lifetime.
About 360 million people are chronically infected carriers of the illness, the majority of whom are ignorant of their HBV status, and approximately 20% – 30% of them will die from chronic complications.
The prevalence of HBV infection varies by nation, reflecting a complex interplay of behavioural, environmental, and host factors. Chronic HBV infection can progress to hepatocellular carcinoma after 20 years; the risk of premature death from cirrhosis or hepatocellular carcinoma ranges between 15% and 25%.
Hepatitis B is a liver inflammatory illness caused by infection with the hepatitis B virus. According to WHO (2002), hepatitis can be caused by medicines or viral agents, which include the hepatitis A, B, C, D, E, F, G, and H viruses.
Hepatitis B is one of the world’s most dangerous diseases. Over a billion people worldwide have serological evidence of hepatitis B virus (HBV) infection, either past or present.
According to research by (White and Fenner (1994), Platkov et al (2001), Carriapa et al (2004), Fernandez et al (2006), and Onuzulike and Ogueri (2007), around 300 million people are chronic carriers of the virus. The rapid spread of HBV demonstrates that it is highly communicable.
According to WHO (2002), HBV infection can be transmitted from mother to child (vertical transmission), 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 immunisation, education, blood and blood product screening, and therapy (CDC, 2005).
According to Anderson and May (1991), epidemiological models serve to capture infection or disease transmission mechanisms in a population in a mathematical framework in order to anticipate disease progression through the population.
1.2 Statement of Problem
The widespread prevalence of HBV in Nigeria and most African countries prompted the study. To combat HBV, the federal government of Nigeria and the World Health Organisation (WHO) have launched a number of initiatives through Nigeria’s Ministry of Health.
Second, mathematicians from all around the world have developed various models to help solve the model and simulate the spread of HBV; nevertheless, many of these models have failed.
1.3 Aims and Objectives of the Study
The primary goal of this research is to analyse the modelling and simulation of HBV dissemination with infectious latent. Other specific study objectives include:
1. Determine the existence and uniqueness of the solution to the model.
2. Conduct a sensitivity analysis on Ro to determine which parameter is the most sensitive and should be targeted for intervention.
3. To investigate the local stability of the model equation using the modified implicit function theorem.
1.4 RESEARCH QUESTION.
The study developed research questions to determine the above-stated aims. The research questions are listed as follows:
1. How can I determine whether the model’s solution exists and is unique?
2. How can I conduct a sensitivity analysis on Ro to determine which parameter is most sensitive and should be targeted for intervention?
3. How do I use the modified implicit function theorem to determine the model equation’s local stability?
1.5 Significance of the Study
The study on modelling and simulating the spread of HBV disease with infectious latent will be of immense benefit to the Ministry of Health of Nigeria, the World Health Organisation (WHO), and other researchers that wish 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 is most sensitive and that
1.6 SCOPE OF THE STUDY
The research on modelling and simulation of the development of HBV disease with infectious latent will address the fields 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 targets the liver and can result in both acute and chronic illness. The virus spreads by contact with an infected person’s blood or other bodily fluids.
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