Fractional mathematical model for the dynamics of pneumonia transmission with control using fixed point theory

This study looks at key epidemiological details of pneumonia by using a mathematical model that includes fixed point theory and fractional-order calculations to see how treatment and vaccination affect transmission. Using fixed point theory for numerical simulations, it is easy to show the relationship between pneumonia dynamics and the different values and parameters in fractional-order models. Through more analyses, it has been shown that both rising contact and weaker treatment would result in an increase in pneumonia cases. Also, the study shows that increasing the numbers of vaccinated and treated individuals can fight and reduce the occurrence of the disease among humans.