Mathematical Modeling of Tuberculosis Dynamics in Care Institutions a Perspective of Variance in Treatment
Kavoyo Kyalo *
Department of Basic Sciences, Faculty of Physical Sciences, Engineering and Technology, Tharaka University, Tharaka Nithi, Kenya.
Ngari Charles
Department of Pure and Applied Sciences, School of Pure and Applied, Kirinyaga University, Kerugoya, Kenya.
Jomba Jason
Department of Basic Sciences, Faculty of Physical Sciences, Engineering and Technology, Tharaka University, Tharaka Nithi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
For many years, tuberculosis has caused millions of deaths worldwide each year. Care institutions are associated with high rate of TB transmission due to the congestion nature in these institutions. The problem encountered by scientists while trying to quit this fatal bacterial disease is insufficient information about the TB dynamics. Most of the researchers provided general information on the TB dynamics mostly touching the TB transmission dynamics. More research is needed for the knowledge gap specifically on TB dynamics in care institutions a perspective of variance in treatment. The objective of the study was to develop mathematical model of tuberculosis dynamics in care institutions a perspective of variance in treatment. The model showed the influence of variance treatment in care institutions. The ordinary differential equations were used for both partial and full treatment in the care institutions. Parameters were varied in each compartment to confirm the sensitivity of the model. The basic reproduction number obtained was used to determine the stability of the model. The findings of these investigations were graphically presented. It was discovered that when full treatment is applied in care institutions, tuberculosis transmission is reduced. Full TB treatment should be done in the care institutions through provision of health care givers who will create awareness on the importance of adherence to medication by those in care institutions. The results of this study will provide valuable information to stakeholders, inform laboratory technicians and field experts by demonstrating the effects of care institutions on the spread of TB and aid in development of new intervention strategies which will help to reduce the spread of TB during outbreak that will otherwise remain unknown leading to better designs for future experiments.
Keywords: Tuberculosis, dynamics, care institutions, normal environments, partial treatment, full treatment