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

Abstract

Pneumonia remains a significant global health concern, claiming millions of lives annually. This study introduces a novel approach by developing and analyzing a Caputo fractional order pneumonia infection model that incorporates pneumonia asymptomatic carriers. Through a qualitative lens, we establish the existence and uniqueness of model solutions by applying the well-known Picard–Lindelöf criteria. Employing a next-generation approach, we compute the model's basic reproduction number, determine equilibrium points, and probe their stabilities. The main objective of this study is to investigate the transmission dynamics of pneumonia infection with a focus on asymptomatic carriers using fractional order modeling. Our findings reveal innovative outcomes as we showcase numerical simulations, providing a practical verification of the qualitative results. Notably, we explore the fractional order model solutions in-depth, examining the influence of specific model parameters and fractional orders on the dynamics of pneumonia disease transmission. The significant contributions of this study lie in advancing the theoretical foundation of infectious disease modeling, particularly in the context of pneumonia. Through rigorous analysis and numerical simulations, we provide valuable insights into the behavior of the proposed fractional order model. These findings hold practical implications for understanding and managing pneumonia transmission in real-world scenarios. Our study serves as a vital resource for researchers, policymakers, and healthcare practitioners involved in combating and preventing the spread of pneumonia, ultimately contributing to global efforts in public health.