Mathematical Modeling of Leptospirosis With Misdiagnosis

Leptospirosis is a widespread zoonotic bacterial disease that continues to pose a major public health challenge, particularly in developing countries where it causes substantial morbidity, mortality, and economic losses. A key problem in controlling the disease is misdiagnosis, which delays appropriate treatment and facilitates continued transmission. Understanding the impact of diagnostic errors is therefore critical for effective disease management and policy planning. In this study, a compartmental epidemic model was developed to examine the effects of misdiagnosis on the transmission dynamics of leptospirosis. The model incorporates disease progression, treatment, and misdiagnosis pathways and was rigorously analyzed for positivity, boundedness, equilibrium points, and their stability properties. The basic reproduction number was derived using the next-generation matrix approach, and numerical simulations were carried out using MATLAB to support the analytical findings. The results show that increased rates of misdiagnosis significantly raise the effective reproduction number, accelerate disease spread, and weaken the effectiveness of treatment interventions. These findings demonstrate that diagnostic accuracy plays a crucial role in leptospirosis control and that failure to correctly diagnose cases can undermine public health efforts. The study underscores the importance of improved diagnostic tools, enhanced clinical awareness, and timely treatment in reducing disease transmission and informing effective intervention strategies for health practitioners, policymakers, and public health organizations.