MATHEMATICAL MODELLING ON THE IMPACT OF HOSPITALIZATION IN THE MANAGEMENT OF TYPHOID FEVER

Abstract

Typhoid fever disease is an infectious ailment which mostly leads to diarrhoea, headache, high fever and stomach pains. This disease is majorly caused by a bacterial infection known as Salmonella typhi. Typhoid fever has caused a significant burden in most developing countries hence a concern to the health sector. In this thesis, a mathematical model has been developed, and based on the ordinary differential equations; the mathematical model is analyzed quantitatively basing on the impact of hospitalization in the management of typhoid fever disease. Hospitals play a big role in the control of typhoid fever through their admission of patients and treatment; therefore, in this thesis a model is developed which explains the effect of increasing hospitalization. The invariant region is worked out in which the model solution is bounded so as to obtain the feasible solution of the set. The next generation matrix method is used to attain the basic reproduction number. The disease free equilibrium and the local stability of the disease free equilibrium determined. The numeric results obtained are determined graphically by use of maple simulation method. The results indicated that; the rate of hospitalization is inversely proportional to the rate of infections while there is a constant rise in the carrier population.