Analysis of a Comprehensive Mathematical Model for Leptospirosis Dynamics: An Optimal Control Application

Abstract

The emergence and re‐emergence of infectious diseases present a major challenge to global public health. Leptospirosis is one of the significant public health issues in tropical regions worldwide; nevertheless, insufficient awareness has resulted in the under‐reporting of its actual incidence and mortality rates. This study presents a comprehensive mathematical model for leptospirosis to analyze the transmission dynamics of the disease. We further explored the model to assess the effectiveness and cost‐effectiveness of different intervention strategies to combat the epidemic. The next‐generation matrix approach is applied to derive the basic reproduction number ( R 0 ) of the formulated model. The model has a disease‐free equilibrium, which is globally asymptotically stable when R 0 < 1. Based on the bifurcation analysis of the model, it is demonstrated that the endemic equilibrium of the model is globally asymptotically stable when R 0 exceeds one. Sensitivity analysis is conducted using a normalized forward sensitivity index to illustrate the impact of model parameters on disease dynamics. Furthermore, the effects of intervention strategies on the spread and overall impact of the epidemic are examined through the application of optimal control theory. The optimal system is simulated using the Forward‐Backward Sweep method implemented in MATLAB. Numerical results show that strategy 8, which incorporates all control measures—wearing protective clothing, washing hands with soap and water after handling rodents, treatment efforts, and rodenticide—is the most effective in controlling leptospirosis. Meanwhile, strategy 2, which includes only washing hands with soap and water after handling rodents and rodenticide, is the most profitable regarding the implementation costs of the strategies.