Optimal control and sensitivity analysis of an SEIHR TB-COVID-19 coinfection model with cost intervention strategies

Abstract A compartmental extended SEIHR-based model is developed to simulate the transmission of TB and COVID-19. The positivity and boundedness of the model are demonstrated. The Basic Reproduction Numbers ( $$R_{0T}$$ and $$R_{0C}$$ ) are calculated for TB and COVID-19 models using the Next Generation Matrix (NGM) method. The individual models exhibit backward bifurcation when $$R_{0T}$$ , $$R_{0C}$$ < 1. The local stability analysis is performed by using Lienard-Chipart criteria. Sensitivity analysis is conducted using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) methods. Optimal control analysis is performed to evaluate the effectiveness of interventions. The co-infection model showed that mask usage significantly reduces both infections. The LHS-PRCC analysis revealed that variables with low p-values strongly influenced the model. Key parameters, including inflow rate, COVID-19 transmission and hospitalization rate, and co-infection progression, exhibited strong correlations. Optimal control measures, including isolation, testing, and treatment, effectively reduced contact between COVID-19-exposed and TB-infected individuals. Post-isolation played a pivotal role in strengthening immunity and aiding recovery from the disease. Implementing all control strategies mitigated the growth of infections and accelerated their decline. The cost-effective analysis, by implementing all interventions, markedly reduces the disease burden (Infection Averted Ratio = 23.72%) and is the most cost-effective strategy, exhibiting a dominant ACER (Average Cost-Effectiveness Ratio) of 0.000359. Finally, we compared the proposed model with the existing coinfection model and validated it with real-time data of individual models.