Optimal Control and Cost-Effectiveness of Vaccination and Treatment for Cholera-Hepatitis E Co-Infection

Abstract

Observational evidence confirms the essential role of vaccination and treatment in reducing and potentially eliminating cholera and hepatitis E virus (HEV) infections. Mathematical modeling is a powerful tool for identifying effective strategies to control disease transmission. This study develops a detailed mathematical model to describe the dynamics of cholera-HEV co-infection, incorporating vaccination and treatment as time-dependent control measures. To ensure the model's validity, key mathematical properties such as positivity and boundedness are examined, confirming that the system is well-posed. The control reproduction number $\left({ℛ}_c\right)$ is calculated using the next-generation matrix method, and both disease-free and endemic equilibria are analyzed. Results show that the disease-free equilibrium is locally and globally asymptotically stable, while the boundary endemic equilibria also exhibit global stability. Sensitivity analysis using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) identifies parameters that most influence ${ℛ}_c$. The model is extended to simulate dynamic intervention strategies, including vaccination and treatment. Numerical simulations support the analytical results, demonstrating how these strategies reduce infection rates in both singly and co-infected populations. Simulations without treatment show an initial rise in infection levels, followed by a gradual decline. This highlights the importance of therapeutic measures, though their effectiveness may be limited by issues such as drug resistance and limited vaccine access. These findings emphasize the need for integrated intervention strategies, especially in light of reinfection cases reported in the literature. Finally, cost-effectiveness analysis shows that treatment-only strategies offer the highest economic efficiency, making them the most favorable option among the interventions evaluated. These insights can help policymakers make balanced, practical decisions when adjusting preventive measures for cholera and HEV control.