Mathematical model and backward bifurcation analysis of pneumonia infection with intervention measures

The main goal of this paper is to build a nonlinear compartmental pneumonia infection model and examine the impact of treatment, immunization, and preventative measures (such as maintaining excellent cleanliness, avoiding close contact with patients, and restricting smoking). The developed model exhibits two different types of equilibrium points: endemic and disease-free pneumonia equilibrium points. In order to confirm that the pneumonia model displays the phenomena of backward bifurcations whenever its effective reproduction number is less than unity, we have employed the center manifold criteria. This finding leads us to the conclusion that lowering the basic reproduction number of pneumonia infections does not ensure that the infection will be completely eradicated in the community. But as this paper's conclusion shows, reducing the rate at which pneumonia spreads has a significant impact on community-wide pneumonia infection control. Sensitivity analysis research reveals that altering the qualitative dynamics of pneumonia infection is mostly dependent on the transmission rate of the illness. Ultimately, based on the outcomes of numerical simulations, we deduce that the most effective ways to reduce the spread of pneumonia in the community are through immunization, treatment, and prevention.