Abstract
In this Research paper, we proposed mathematical modeling of gonorrhea infection treatment dynamics with incorporating control individual class. We obtained the Disease Free Equilibrium State and Endemic State. The criterion for stability of the Disease Free State was established using the reproduction number R0 . The model equations were solved using Homotopy Perturbation
Method. The result of the numerical simulation shows that at high treatment rate of the gonorrhea Disease can be eradicated completely which will also eradicate the transfer of the disease to Human
CHAPTER ONE
Introduction
1.1 Background of study
Gonorrhea is a sexual transmission infectious disease; it is caused by a bacterium known as Neisseria gonorrhea, which invades the genital organs and reproductive track causing inflammation of the tube which carries sperm and infertility (Oworu et al., 2013). New cases of gonorrhea diagnosed each year are estimated to be 78 million; in the united states alone there an estimated 820,000 new gonorrhoea infections each year while in 9963, WHO found Logos (Nigeria) to have the highest gonorrhea in the world (Ogunbanjo BO 1989 and Lorismith 2018). Historically, gonorrhoea was discovered in 1792, in Edinburg where the surgeon Benjamin Bell clearly differentiated it from syphilis infectious disease (Benedek, 200). It does not only invade the reproduce track, but can also attack throat, mucous membranes of the eyes, throat, mouth rectum and anus (Lorismith 2018). Untreated gonorrhea in female may lead to pelvic inflammatory disease (PID) which causes permanent damage to the reproductive organ leading to infertility while in male it develops an epididymitis condition while causes fever, severe pain and swelling (Los olivos women’s medical group, 2019). Gonorrhea is transmitted sexually through the penis, vagina, mouth or anus of infected individuals spread of gonorrhoea does not depend on ejaculation; it does not have to occur for gonorrhea to be spread of acquired. Gonorrhea can also be transmitted prenatally from infected mother to baby during child delivery. The treated individuals may be reinfected if sexual contact occurs between them and infected person (CDC, 2016). Untreated gonorrhea infections in human increase a person’s risk of acquiring or transmitting HIV, which may lead to AIDs (Flaming et al., 1999). If a child contacts gonorrhea from infected mother during childbirth, it can cause blindness, joint infection in the body or a life threatening blood infection in the child, urgent treatment of gonorrhea infection in pregnant woman as soon as it is discovered reduces the risk of above complications.
Gonorrhea is a major public health challenge today, due to the high incidence of infections accompanied by a dwindling number of treatment options (Schiffert Health Center, 2011). It is a sexually transmitted disease caused by a type of germ, bacteria called Neisseria gonorrhea. It is passed from one person to another during vaginal, anal and oral sex (Amalia, G. & Loukas, Z., 2015). Gonorrhea is one of the sexually lethal transmitted diseases (STD) due to the number of complications that it causes in the infected persons (Sacrifice, N. K., et al., 2016; Riley, S., 2010). The disease has an incubation period of 10 days in women and 2-5 days in men (Balmelli, C. & Guntlard, H. F., 2003), and it was estimated that, approximately 106 million new cases of gonorrhea among adults globally was estimated (Benedek, T. G., 2005). The bacteria can be found in the throat, vagina, Urethra, and anus (Mushayabasa, S., et al., 2010). The history of the discovery of the neisseria Gonorrhea infection can be traced to Edinburg in the year 1792, where the surgeon Benjamin Bell clearly differentiated it from syphilis infection (Benedek, T. G., 2005). Gonorrhea causes a lot of complications in the infected persons, and a prolong infection can lead to severe eye infections, infertility in both men and woman, ectopic pregnancy, spontaneous abortion, still births and eventually death if untreated (Riley, S., 2010). The bacteria targets the cells of the mucous membranes, including the surfaces of the Urethra, vagina cervix, anus, rectum, the lining of the eyelid and the throat (Schiffert Health Center, 2011). Behavioral change is very important in the control of the spread of diseases and as such, can be involved in the interpretation of the diseases outbreak data and estimation of decreases transmission rates (Prabhakararao, G., 2013).
The epidemiology of infectious diseases has moved beyond identifying etiological agents and risk factors to a more detailed understanding of the mechanisms for controlling the distribution of infections (Garnette, G. P., 2002). Mathematical models provide an explicit framework to study the transmission dynamics of infectious diseases (Garnette, G. P., 2002). In 2013, Prabhakararao developed a mathematical model for the transmission dynamics of gonorrhea infection in Anantapur District, Andhra-Pradesh-India. In developing the model, they partitioned the population into susceptible, infectious and removed compartments and assumed recovery from infection confers permanent immunity.
The result of their study showed that the epidemic does not die out, but ultimately approach a steady state with reference to its severity among the population of Anantapur District. A more robust study was carried out by Ana, L. & James, A. Y. in 1976, where they took into consideration the fact that; the spread of gonorrhea in a population is nonuniform, and by partitioning the population into n groups they developed a deterministic model for Gonorrhea in a non-homogenous population. They carried out a study of the asymptotic stability properties of the model, to show that the disease will die out either for all positive initial disease levels or for none, depending on the contact rates and the lengths of infectious periods. Furthermore, they showed that if the initial number of infectives in at least one group is not zero, then the disease will remain endemic and the number of infectives in each group will approach a constant positive level. They concluded that; this behavior of gonorrhea epidemics is different from most other infectious disease, which usually have occasional major outbreaks followed by low disease levels, and that this different behavior of gonorrhea is attributable to the lack of developed immunity and the basic non seasonality of the disease. The major signs and symptoms of gonorrhea includes Vagina discharge, burning during urination, low abdominal pain, pus discharge from the male genital organ or bleeding, unusual sores, inflammation of the genital organ (Oworu et al., 2013). can cause blindness, joint infection in the body or a life threatening blood infection in the child, urgent treatment of gonorrhea infection in pregnant woman as soon as it is discovered reduces the risk of above complications. The major signs and symptoms of gonorrhea includes Vagina discharge, burning during urination, low abdominal pain, pus discharge from the male genital organ or bleeding, unusual sores, inflammation of the genital organ (Oworu et al., 2013).
The surest way to prevent transmission of gonorrhea or other sexually transmitted diseases is to abstain from sexual activities or to be a long term mutually monogamous relationship with a tested partner who is uninfected (CDC, 2016). According to (Semchenko EA, et al, 2018) Bersero is a meningococcal B vaccine approved in the united states since 2015, induces antibodies in humans that target Neisseria gonorrheae. Kate L, Seib, PhD, associated professor and research leader in the institute for glycomics at Griffith university in Southport, Australia, and colleagues the ability of Bexsero (Glaxosmith Kline) to illicit and immune response against N. gonorrhea and discovered it very protective. The vaccine was approved in the U.S for people between 10 to 25 years (Semchenko EA, et al, 2018). According to (Leung et al., 2012), developed a continuous transmission among homosexuals. They equally applied a non – standard discretization method to formulate a discrete time model and the results of their models were compared.
1.2 Statement of the Problem
Gonorrhea, a sexually transmitted infection (STI) caused by the bacterium Neisseria gonorrhoeae, remains a significant public health challenge, particularly in regions with high transmission rates. Rivers State, Nigeria, is among such regions where gonorrhea prevalence has shown alarming trends in recent years. The rapid transmission, coupled with the emergence of antibiotic-resistant strains, has compounded the challenges of controlling the spread of the disease. Current prevention and treatment strategies may not be sufficient in containing the epidemic. Despite ongoing public health interventions, there remains a need to better understand the transmission dynamics of gonorrhea in this region. Mathematical modeling offers a powerful tool to investigate the factors driving the spread of the infection, evaluate the impact of interventions, and guide resource allocation. This study aims to develop a mathematical model that captures the transmission dynamics of gonorrhea in Rivers State, providing insights into effective control strategies.
1.3 Research Objectives
1. To develop a compartmental mathematical model that describes the transmission dynamics of gonorrhea in Rivers State, Nigeria.
2. To analyze the model to determine the basic reproduction number (R₀) and other key parameters influencing the spread of gonorrhea in the population.
3. To simulate various public health intervention strategies (e.g., increased testing, treatment, and public education campaigns) and assess their potential impact on reducing gonorrhea transmission in Rivers State.
1.4 Justification of the Study
The persistent rise in gonorrhea cases in Rivers State, coupled with the global concern over antibiotic resistance, necessitates innovative approaches to disease control. Mathematical modeling is an invaluable tool in epidemiology that can help predict disease behavior, identify key transmission factors, and test the effectiveness of various interventions before implementation. By providing a deeper understanding of gonorrhea transmission dynamics in the local context, this study will contribute to more effective public health strategies and inform policy decisions aimed at reducing the burden of the disease. Furthermore, the results of this study will provide a scientific basis for optimizing resource allocation in gonorrhea prevention and control programs, ultimately contributing to better health outcomes for the population of Rivers State.
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