Mathematical Modelling on the Impact of Hospitalization in the Management of Typhoid Fever
Keywords:
Mathematical Modelling,, Hospitalization,, Management & Typhoid FeverAbstract
Typhoid fever disease is an infectious ailment which mainly leads to diarrhoea, headache, high fever and stomach pains. This disease is mainly 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. A deterministic 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, a model developed explains the effect of increasing hospital management on patients having this disease. 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 is further determined qualitatively and the local stability of the disease free equilibrium is determined. The results obtained are determined graphically by use of maple simulation method. From the graphical numeric results, the results were analyzed, discussed and conclusions made. The results indicated that the rate of hospitalization is inversely proportional to the rate of infections. From the numeric results obtained, recommendations were made
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