MATHEMATICAL MODELLING ON THE TRANSFER OF HIV/AIDS BASED ON SEX GROUPS
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ABSTRACT
In this project, a mathematical model connecting the occurrence of HIV/AIDS transmission with the number of infected and uninfected individuals was used to describe the occurrence of HIV/AIDS transmission in different sex groups. The study was conducted using data from BarauDikko Teaching Hospital Kaduna, Kaduna State. In this research the rate of infection for the various sex groups were calculated and analyzed. Graphs were plotted to show the rate of infection in males and females, then an extra graph was plotted to show which sex group had more infected individuals. The result of the analysis shows that the occurrence is almost the same in the spread of the virus among the different sex groups in the period of study but it is higher in that of females. It is concluded that HIV/AIDS is a killer disease claiming larger number of lives every day. Therefore, all hands must be on deck by government and non-governmental organizations to minimize the rate of spread of the killer disease.
DECLARATION.. ii
CERTIFICATION.. iii
DEDICATION.. iv
ACKNOWLEDGEMENT.. v
ABSTRACT.. vi
TABLE OF CONTENTS. vii
CHAPTER ONE.. 1
GENERAL INTRODUCTION.. 1
1.1 Background of the Study. 1
1.2 Transmission of HIV. 2
1.3 Test for Identification of HIV. 3
1.4 Signs and Symptoms of HIV. 3
1.5 Control and Treatment of HIV. 4
1.6 Prevention/Vaccine of HIV. 6
1.7 Brief Story of HIV in Kaduna State. 6
1.8 Scope and Limitation of Research. 7
1.9 Statement of the Problem.. 7
1.10 Aim and Objectives of the Study. 7
1.11 Definition of Terms. 8
1.11.1 Dynamical system.. 8
1.11.2 Mathematical model 8
1.11.3 Model Validation. 9
1.11.4 Model 9
CHAPTER TWO.. 10
LITERATURE REVIEW… 10
2.1 Introduction. 10
CHAPTER THREE.. 13
METHODOLOGY.. 13
3.1 Introduction. 13
3.2 Model Formulation. 13
CHAPTER FOUR.. 18
ANALYSIS AND DISCUSSION OF RESULT.. 18
4.1 Introduction. 18
4.2 Application of the Model to Different Sex Groups of Individuals. 18
4.2.1 Applying model to male sex. 18
4 .2.2 Applying model to female sex. 21
CHAPTER FIVE.. 29
SUMMARY, CONCLUSION AND RECOMMENDATION.. 29
5.1 Summary. 29
5.2 Conclusion. 29
5.3 Recommendation. 30
REFERENCES. 32
CHAPTER ONE
GENERAL INTRODUCTION
1.1 Background of the Study
Human Immunodeficiency Virus (HIV) is a highly complex and potentially life-threatening virus that primarily attacks the immune system, specifically targeting CD4+ T cells, which play a crucial role in the body’s ability to fight off infections. HIV weakens the immune system over time, leaving the infected individual more vulnerable to various infections and diseases.
HIV is a member of the retrovirus family and is transmitted through certain body fluids, such as blood, semen, vaginal fluids, breast milk, and rectal fluids. The most common modes of transmission include unprotected sexual intercourse with an infected person, sharing contaminated needles or syringes for drug use, and from an infected mother to her child during childbirth or breastfeeding.As HIV gradually damages the immune system, the individual becomes susceptible to various opportunistic infections and certain types of cancer. Without proper medical treatment, the infection progresses to the final stage known as Acquired Immunodeficiency Syndrome (AIDS). At this point, the immune system is severely compromised, and the individual becomes vulnerable to life-threatening infections and illnesses.However, with advancements in medical science, there are highly effective antiretroviral therapies (ART) available that can effectively control HIV replication, slow down disease progression, and improve the quality of life for those living with HIV. While ART cannot cure HIV, it has transformed HIV infection into a manageable chronic condition for many people, enabling them to live long and healthy lives. (James N. and Philip M., 2002).
1.2 Transmission of HIV
HIV (Human Immunodeficiency Virus) can be transmitted through certain body fluids from an infected person to an uninfected person. The primary modes of HIV transmission include:
- Unprotected Sexual Contact: HIV is most commonly transmitted through sexual intercourse, particularly unprotected vaginal, anal, or oral sex with an infected partner. The virus can enter the body through small cuts or sores in the mucous membranes of the genital or rectal area.
- Sharing Contaminated Needles and Syringes: HIV can be transmitted through sharing needles or syringes used for injecting drugs, steroids, or medications. This mode of transmission is common among intravenous drug users.
- Mother-to-Child Transmission: An HIV-infected mother can pass the virus to her child during childbirth or through breastfeeding. However, with appropriate medical interventions during pregnancy, childbirth, and breastfeeding, the risk of transmission can be significantly reduced.
- Occupational Exposure: Healthcare workers may be at risk of HIV transmission if they are accidentally exposed to infected blood through needle stick injuries or other sharps injuries. Precautions and post-exposure prophylaxis (PEP) can reduce the risk of infection.
- Needlestick Injuries and Accidental Exposure: People who handle needles or other sharp instruments, such as tattoo artists or body piercers, may be at risk if accidental needlestick injuries occur with an HIV-infected individual. (Michael H. Merson, 2011).
1.3 Test for Identification of HIV
There are several types of tests available for the identification of HIV infection. These tests are designed to detect the presence of HIV antibodies, antigens, or genetic material (RNA/DNA) in a person’s blood or other body fluids. The most common types of HIV tests include
- HIV Antibody Tests,
- ELISA (Enzyme-Linked Immunosorbent Assay),
- Western Blot,
- Rapid Antibody Tests,
- HIV Antigen Tests,
- HIV RNA/DNA Tests,
- Home HIV Test Kits.
It’s essential to remember that no HIV test is 100% accurate immediately after infection. If there’s a recent exposure and the test result is negative, it’s recommended to repeat the test after the window period (usually 3 months) to confirm the result.
1.4 Signs and Symptoms of HIV
HIV is a virus that attacks the body’s defense system, called the immune system. It makes it harder for your body to fight off infections and illnesses.When a person gets infected with HIV, they may go through different stages. In the beginning, they might experience flu-like symptoms, such as fever, tiredness, sore throat, and swollen glands. But some people may not have any noticeable symptoms at all.After this early stage, HIV can stay in the body for a long time without causing any major problems. During this time, the person may not feel sick, but the virus is still there and can be passed on to others.
As the infection progresses, the immune system gets weaker, and the person becomes more vulnerable to infections and other health issues. This is the stage called AIDS (acquired immunodeficiency syndrome). At the AIDS stage, the person might experience more severe symptoms, like significant weight loss, chronic diarrhea, fever, night sweats, and frequent infections that don’t go away easily. It’s important to remember that not everyone infected with HIV will have the same symptoms or go through all the stages. Some people
may not even realize they have HIV because they feel fine. Finally, the best way to know if someone has HIV is to get tested. Testing can help detect the virus early, and if HIV is diagnosed, there are effective treatments available to manage the infection and live a healthy life.
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