Modeling the Transmission of Tuberculosis Meningitis Disease with Optimal Control Strategy
DOI:
https://doi.org/10.62054/ijdm/0302.14Abstract
Mycobacterium tuberculosis causes Tuberculosis Meningitis (TBM) which is a life-threatening infectious disease that leads to inflammation of the membranes surrounding the brain and the spinal cord. It remains a major public health challenge due to its high rates of mortality and long-term neurological disability. Though various clinical studies have been done to alleviate its burden, little focus has been put on deterministic mathematical modelling and optimum cost-effectiveness analysis of its transmission dynamics. This paper presented a deterministic mathematical model of the transmission dynamic of tuberculosis meningitis to explore optimal control methods and cost-efficiency of control. The model has been developed as a set of ordinary differential equations. The autonomous version of the model was subjected to qualitative analysis. Next Generation Matrix method was used to calculate the basic reproduction number and sensitivity analysis carried out to find out how important model parameters affect reproduction number. Moreover, Pontryagin’s Maximum Principle was used to perform a detailed analysis of the non-autonomous optimal control model with three control interventions. Incremental Cost-Effectiveness Ratio was calculated in order to assess the economic efficiency of the suggested control strategies. Analytical results were illustrated using numerical simulations to determine the most cost-effective strategy of preventing and controlling tuberculosis meningitis.
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