Fractional optimal control and cost-effective analysis of community-acquired pneumonia

Community-acquired pneumonia (CAP) is a common respiratory infection that happens outside of hospitals, and it is caused by bacteria, viruses, or fungus. It remains a serious threat to the world, particularly affecting children, the elderly, and immunocompromised individuals. The fractional-order pneumonia model has been developed in this study to determine the disease dynamics in the system. The model stability is proved for the existing equilibrium points. Global sensitivity analysis was carried out utilizing Latin hypercube sampling (LHS) and partial rank correlation coefficient (PRCC) to find the key parameters influencing disease transmission. Control analysis is considered as an effective strategy for preventing the spread of the disease pneumonia. It is often necessary to combine timely treatment, immunization, and boosting immunity. However, eliminating this disease in the population will be challenging if control strategies aren’t given at the appropriate time and in sufficient quantity. We conduct a cost-effectiveness analysis of four optimal control strategies utilizing numerical methods. Our findings indicate that vaccination is the most cost-effective and efficient control intervention among the strategies compared.