Modeling and analysis of tuberculosis and pneumonia co-infection dynamics with cost-effective strategies

Abstract

Tuberculosis and Pneumonia are among the major airborne diseases that shares common clinical traits with high human morbidity and mortality impacts. Thus, the co-infection of the two diseases becomes unavoidable in a community of comorbid populations. Due to scare resources, the huge disease burden co-imposed by these endemics requires an effective intervention to cushion the effect. To achieve this goal, cost–benefit analysis for the optimal controls is deemed necessary. In this study, an SEIR model for the co-dynamics of tuberculosis and pneumonia is formulated. The model was shown to have a globally stable disease-free (endemic) equilibrium where the reproduction number is less (greater) than unity. Sensitivity analysis by partial rank correlation coefficients shows that increasing infection recovery is only one among the three most influential parameters that reduces the magnitude of the diseases. Through Pontryagin′s maximum principle, the number of infected individuals and cost of controls (public health campaign, chemoprophylaxis, oral fluid intake and treatment) was minimized. In implementing the cost–benefit analysis, we employ three techniques: the Infection Averted Ratio (IAR), the Average Cost-effectiveness Ratio (ACER) and the Incremental Cost-effectiveness Ratio (ICER). On comparing the strategies considering cases (A–E), the ICER results showed that, strategy with treating tuberculosis alone is the most effective and cost-saving strategy. But in terms of infections averted, strategy with all the control measures is the best; however, unaffordable since it is highly expensive. We hope that, the findings of this study should help policy-makers when dealing with the co-existence of tuberculosis and pneumonia.