Mathematical modeling and optimal control of leptospirosis transmission considering temperature dependent growth rate of bacteria
摘要
Leptospirosis is an emerging zoonotic disease that poses significant threat to public health and economy. The main objective of this work is to analyze the dynamics of leptospirosis disease considering temperature dependent growth of bacteria with optimal control. The existence and stability conditions of the equilibrium states are analyzed in relation to the basic reproduction number. To assess how well the model represents reality, we calibrated it using actual leptospirosis case data from Kerala, spanning from January 2018 to December 2023. Through sensitivity analysis, we identified the most influential model parameters of the disease control and found that the temperature-dependent bacterial growth rate is among the most critical. Further, study considers three types of control measures: a prevention strategy targeting susceptible humans, medical treatment for those infected and proper sanitation of the environment. Pontryagin’s Maximum Principle has been employed to determine the most effective control strategy for reducing the leptospirosis infections. The numerical results show that integrating treatment, prevention and environmental sanitation as control measures proves to be the most effective strategy for minimizing the impact of the disease within the community. The combined control measures yields approximately a reduction of 36.4% in the peak number of infected individuals.