Local Stability Analysis of Leptospirosis SEITR - SI Model with the Influence of Hydroclimatic Rate and Treatment - Ega Ananta Erlangga; Budi Priyo Prawoto (ZERO: Jurnal Sains, Matematika dan Terapan, 2026)
Leptospirosis is a zoonotic disease whose transmission is influenced by interactions between humans, vectors, and environmental conditions. This study proposes a novel SEITR–SI model that simultaneously integrates treatment dynamics and hydroclimate-dependent transmission within a single analytically tractable framework. Unlike previous SEIR–SI and SIR–SI formulations that either exclude treatment or incorporate hydroclimatic effects through explicit environmental compartments, the proposed model represents hydroclimatic influence implicitly through transmission intensity while preserving mathematical simplicity. The local stability of the disease-free and endemic equilibria is analyzed using the basic reproduction number  and the Routh–Hurwitz criterion. The analysis confirms classical threshold behavior governed by , while numerical simulations reveal that increased hydroclimatic transmission intensity elevates endemic infection levels even under higher treatment rates. These findings highlight that treatment alone may be insufficient in hydroclimate-sensitive environments and underscore the importance of integrated control strategies combining medical intervention with environmental and vector management.