Optimizing Protection and Treatment Strategies for Childhood Pneumonia amid Vaccine-Unresponsive Serotypes

A mathematical model integrating both vaccination and treatment strategies for childhood pneumonia is developed to assess conditions for effective disease control. Special attention is given to individuals who do not respond to the vaccine, and their role in pneumonia transmission dynamics is analyzed. The effective reproduction number is derived, and conditions for the asymptotic stability of both the disease-free and endemic equilibria are established. An optimal control analysis is conducted to determine the most effective strategies for minimizing pneumonia cases. Three time-dependent control measures are considered: 1) pneumonia prevention, 2) identification and treatment of carriers, and 3) enhanced treatment of infected individuals. Numerical simulations and sensitivity analysis reveal that while vaccination and treatment significantly reduce pneumonia prevalence, the presence of vaccine-unresponsive serotypes poses a challenge to disease eradication. Additionally, results indicate that implementing multiple control strategies is more effective than relying on a single intervention. A combination of all three measures yields the best outcomes in reducing both infection and carriage rates.