A mathematical model for measles transmission with optimal interventions and cost–effectiveness analysis

Measles remains a significant public health barrier despite advances in vaccines, particularly in settings where immunization is not widespread. For this research, we discuss – and analyze a compartmental mathematical SIR model of measles transmission that incorporates time-dependent control measures modeling increased first-dose vaccination efforts, reduced effective contact rates, and enhanced in-patient care. Our mathematical analyses include finding the region that is invariant, finding the disease-free stationary solution for the control system with disease, and finding the value of $$R_C$$ using a next-generation matrix approach. We formulated an optimal control problem to minimize the burden of infection and hospitalization costs as well as control implementation expenses. The optimal control conditions are solved using Pontryagin’s Maximum Principle. Global sensitivity analysis with Latin hypercube sampling and partial rank correlation coefficient analysis was employed to explore the main drivers of the disease dynamics and the controlled reproduction number. Results obtained suggest that vaccination by itself has been found to have very limited effects in controlling active cases, reducing contacts results in a significant decrease in infections, and better treatment results in easing the burden on hospitals. The holistically optimum strategy would be to adopt all measures – vaccination, contact reduction, and treatment – which will be most successful in controlling the prevalence rate. The application of incremental cost-effectiveness ratio to analyze the cost-effectiveness implies that contact reduction is the most cost-effective method in the prevention of measles cases. The findings emphasize the significance of a comprehensive and economically viable approach to measles control.