CHAPTER ONE

INTRODUCTION

1.1 Background of the Study

Typhoid fever is an exclusively human transmitted systemic disease caused by infection with the bacterium Salmonella enterica enterica serovar Typhi. A notable feature of typhoid is the carrier state – asymptomatically infected individuals who continue to shed Salmonella Typhi in their stool or urine for many years, thereby sustaining transmission Nelson (2020). Typhoid fever is a contagious disease found only in human and occurs due to systematic infection mainly by salmonella typhi organism (Mushayabasa (2013). The bacteria are transmitted through food and water contaminated faeces and urine of an infected patient or a carrier (WHO November 2007 meeting, 2007, 11). During and infection, bacterium multiplies in monocular phagocytic cells before being released into the bloodstream (Jenkins and Gillespie Salmonella infection (2009). Typhoid fever attack 21 million people and kills 200,000 worldwide every year. The disease is major problem in most developing countries where there is lack of proper sanitation and occurs due to contaminated water. The most common type of salmonella that causes typhoid fever is Salmonella paratyphi A, B, and C and D, WHO the diagnosis, treatment and prevention of typhoid Fever (2003).

Different models have been developed to analyse the transmission dynamics of typhoid fever as well as the effectiveness of some intervention strategies against the spread of typhoid infections. For instance, Mathematical model transmission dynamics of typhoid is developed in order to evaluate the potential direct and indirect effects of vaccination Pitzer (2014). The model is validated against randomized vaccine trials. It is tested on school-based vaccination strategies, and it is discovered that typhoid vaccination is expected to lead a short-term indirect protection and decrease in typhoid incidences, but vaccination alone is unlikely to lead to elimination of typhoid. A simple mathematical model is developed on direct and indirect protection by vaccine and benefits of generic vaccination program. The population is split into vaccinated and the unvaccinated subgroups and its effectiveness redefined. It is found reduces the number of susceptible to infection and fever infected individuals spread the disease among both vaccinated and unvaccinated persons Cook (2010).

The model is developed by Cvjetanovic (1971). In the models the number of newly infected persons is expressed as a function of the infectious of susceptible people in a community within a given time. The age structures of population are

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established, which enables more detailed simulation of the effect of various interventions and strategies to control the disease in different age groups. The study indicates that once the incidence of the infection has fallen below threshold, it cannot be maintained in a community due to loss of the main source of infection chronic carriers as the die out naturally. Mathematical model for transmission dynamics for typhoid developed in order to evaluate the potential direct and indirect effects of vaccination. The model is validated against randomized vaccine trials and it is evaluated to lead a short-term indirect protection and decrease in typhoid incidences, but vaccination one is unlikely to lead to elimination of typhoid. Both short and long term carriers contribute to transmission, but not necessarily at the same rate as primary infections Pitzer (2014).

1.2 Statement of the Problem

Typhoid fever infects 21 million people and kills 200,000 worldwide every year. Asymptomatic carriers are believed to play a major role in the evolution and global transmission dynamics of Typhoid fever, and their presence greatly hinders the eradication of typhoid fever using treatment and vaccination (Naresh, 2018). The government of Nigeria and the non-government organization (Food for the hungry international) has played a role in providing health facilities and health services in order to eradicate the disease. It is usually a common disease during rainy seasons and as a result water in form of erosion flows to the rivers causing contamination. The health sector reported an increasing number of typhoid cases since June 2018 and the government requested for assistance to control the spread of the disease infection. Typhoid is a dangerous disease on human health. Once a bacteria that causes typhoid is consumed it travels from the digestive system into the blood. As the bacteria travels through the body, symptoms like high fever, head ache and overall fatigue can develop. The digestive is also affected by the bacteria which lead to stomach pain, diarrhoea or constipation and weight loss. The blood can carry the bacteria to the other organs including the lungs, liver, gallbladder and the kidneys. Infection in these organs can cause other problems and symptoms such as pneumonia. It is from these effects that the researcher seeks to find out the solution for this infection and examine the effects of vaccination via mathematical modelling.

1.3 Aim and objectives of the study

The aim of this research project is to modify the ESIT (Exempted Susceptible Infection Treatment) for transmission dynamics of typhoid fever and epidemic dynamics of cholera.

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Thus, the objectives are to

1. the disease-free equilibrium

1. Establish the basic reproduction number

1. Carryout the stability analysis of disease-free equilibrium

1.4 Justification of the study

The research project will be useful in understanding the transmission and spread of typhoid fever which can help the government and non-governmental organization in formulating control strategies. This study will also have an important role in the community towards awareness and public caution about the spread of the infection, the government therefore can rely on these findings to help the groups and individuals concerning this disease.

1.5 Scope and limitation

This research work covers aim and objectives of the study for the model of the transmission dynamics of typhoid fever with vaccinations.

1.6 Operational Definitions of Terms

Immunity: The body’s ability to resist being affected by infection and disease

Population: This is the number of individuals in a given area at a given period of time

Mathematical modelling: This is the art of transforming system into mathematical concepts and language

Susceptible: The compartment of the population that stands the risk of being infected

Exempted: Individuals that are infected but not infectious, it is also referred to as incubation or latent compartments

Infections: The compartments of populations that are infected

Treatment: The compartments were those that are treated at the infections or exempted class.

Vaccination: This is the administration of weakened antigens to produce immunity to a disease

Basic reproduction number: This is the population where those that are treated at exempted class or those treated at the infectious class experience recovery and this research will include those in the susceptible class that are partially immune due to vaccinations60