Speaker
Description
Mathematical models are used to capture the dynamics of diseases. This project seeks to investigate a SIR model for diarrhea infection with treatment as a compartment. Four nonlinear ordinary differential equations for the SITR model with one infective compartment is established. Then the reproductive number R 0 is determined. Mathematical analyses show that the model is locally and globally stable. A sensitivity analysis is performed for the disease transmission, to determine the right parameters responsible for its transmission and prevalence.
The model is fitted to the diarrhea incidence data from 2008 to 2015 by MOH-Ghana for validation. It was observed that the model fits well to the Ghanaian diarrhea incidence data; this shows that the model can also be used in other countries. The trend of diarrhea cases over a long period of time is predicted and the results forecast a decreasing trend. Optimal control analysis is performed to know the efforts needed to control the diarrhea disease.
The analytical results obtain on incorporating the three optimal controls; public health education u_1(t), the minimization of the bottlenecks of administering vaccination u_2(t) such as unavailability of vaccines, inaccessibility to the communities and the minimization of the bottlenecks of the fraction of individuals (infective class) that take oral rehydration therapy (ORT) at home u_3(t), such as: unavailability of ORS component, using untreated water to make up the solution into the model system were verified through simulations. The dynamics of the infected population for different scenarios were discussed. Finally, the simulations show that all the three controls stated above must be used simultaneously for effective controlling of the disease in Ghana.
