Insight into the treatment strategy on pneumonia transmission with asymptotic carrier stage using fractional order modeling approach

•The study formulate pneumonia infection Caputo fractional order model.•The study investigates well-posedness of the model, stabilities of the fractional order model.•The study numerical simulation justifies the qualitative analysis of the model.•The numerical simulation investigates the impacts of fractional orders and some model parameters on the control of pneumonia infection.