An analytical transmission model for evaluating pneumonia vaccination and control strategies

Pneumonia is an infectious disease caused by various agents, such as viruses, bacteria, or fungi. This study proposes an analytical pneumonia model to assess the impact of vaccine interventions. The proposed mathematical model reveals that pneumonia will be eradicated from the population if the basic reproduction number is less than one. Furthermore, our bifurcation analysis indicates the absence of a backward bifurcation, meaning that the basic reproduction number is the sole threshold for determining the endemicity of a disease. In other words, pneumonia will be extinct if the basic reproduction number is less than one and will exist if it is larger than one. We estimate our model parameter values using incidence data from five districts in Jakarta, Indonesia. The dataset consists of weekly incidence data from 2023 until mid-2024. Our analysis shows North Jakarta has the highest case incidence per 100,000 individuals compared to the other districts. A global sensitivity analysis, using the partial rank correlation coefficient and Latin hypercube sampling, was conducted to identify the most impactful parameters on the basic reproduction number for each district in Jakarta. An optimal control problem was formulated to determine the most effective strategies for controlling pneumonia in the field. We found that adult vaccination has a greater impact on reducing the spread of pneumonia than a newborn vaccination strategy. However, combining both newborn and adult vaccinations is essential to ensure long-lasting immunity in children.