A Mathematical Model of the Spread of Pneumococcal Pneumonia Disease by Considering Vaccine and Hospital Care Interventions

Pneumococcal pneumonia is a type of community-acquired pneumonia which is an acute respiratory infection caused by Streptococcus pneumoniae bacteria. In this study, a mathematical model on the spread of Pneumococcal pneumonia is constructed by considering vaccination and hospital care interventions. The model is formed by dividing the human population based on their health status. We consider several things in the model's construction, such as asymptomatic individuals, the latent phase during infection, and interventions of vaccination and hospitalization. Analytical studies are carried out to find and analyze the existence and local stability of the equilibrium points, determining the basic reproduction number (R₀), and investigate the type of bifurcation of the model. We find that the model exhibits a forward bifurcation when R₀ = 1. These result means that we have to reduce the value of R₀ as large as possible using vaccination and/or hospitalization to avoid the existence of Pneumococcal pneumonia in the community. Several numerical experiments are shown to see the visualization of the model. The simulation results show that the rate of vaccination and the rate of hospitalization only have a very significant effect at the beginning in reducing the value of R₀, but not as significant when the value of the two rates given is large enough. It is also concluded that an increase in the rate of vaccination is more successful in reducing the number of individuals infected with Pneumococcal pneumonia compared to an increase in the rate of hospitalization. Thus, it will be more effective for intervention in the field to rely on vaccination compared to hospitalization. The type of vaccine used in the vaccination process also has a significant effect in reducing the value of R₀. This is because the elasticity value of the parameter ζ, which is the infection reduction value because the effectiveness of the vaccine, has the most significant effect in reducing the value of R₀ compared to the parameters that indicate the rate of vaccination and the rate of hospitalization.