Abstract
A bacterial disease called leptospirosis is very typical in both tropical and subtropical regions. It is a well-known animal-borne illness that is brought on by spiral-shaped bacteria (Leptospira spp.). Both directly and indirectly, the disease can spread to humans through the urine of sick animals or polluted water, soil, or food. Two phases might appear in leptospirosis symptoms. The patient will have symptoms such as fever, chills, headache, muscle aches, vomiting, or diarrhea during the first phase, which is known as the Septicemic phase. In the meantime, the Immune phase, the second, is more severe. Meningitis, liver failure, renal failure, or both could be fatal for the patient. This study aimed to create a mathematical model of leptospirosis disease using free-living bacteria. In the model, interactions occur between people, free-living Leptospira, animal hosts, and animal vectors. The population's characteristics are used to build the model, and the actual issue is used to identify the disease's transmission paths. While the endemic equilibrium is investigated numerically, the disease-free equilibrium is analyzed theoretically. The paper demonstrates that for the established mathematical model with an epidemic threshold $R_0$, analytical and numerical solutions produced the same outcome.
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