Effect of vaccination on non-integer dynamics of pneumococcal pneumonia infection

Abstract

Pneumococcal pneumonia is a contagious, possibly fatal bacterial lung infection that can strike at any time and in any place. It can land you in the hospital and possibly put your life in jeopardy in severe situations. Pneumonia can range from a minor illness to a major or life-threatening infection and it can even be fatal. Therefore, it is of great importance to conceptualize the transmission phenomena of this dangerous infection and to provide control interventions. Here, an epidemic model to conceptualize the transmission phenomena of pneumococcal pneumonia with vaccination and treatment factors is structured. The equilibria of the model are inspected and the reproduction parameter (indicated by ℛ0) is determined. Stability results for the equilibria of the system have been proved. The reproduction parameters of the scheme are analyzed numerically with the variation of various input parameters. Moreover, adequate conditions for the uniqueness and existence of the solution to the hypothesized problem of pneumococcal pneumonia infection have been proved. Different simulations of the recommended pneumococcal pneumonia model are performed by changing the input factors to study the complicated dynamics of pneumococcal pneumonia infection with the influence of different input parameters of the system. This article discusses the system's dynamic behavior in order to develop effective infection control policies. Important changes have been observed when the order of the fractional derivative is decreased. This study recommended different factors for the reduction of pneumococcal pneumonia to the policymakers in the community.