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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Budi Priyo Prawoto
Department of Mathematics, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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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 Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28376

Abstract

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.
Modelling Leptospirosis Transmission with Waning Immunity and Stage-Structured Infection: Local stability and Vaccination Analysis Dinta Ardelia Wahyudi; Budi Priyo Prawoto
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i2.30511

Abstract

Leptospirosis remains a complex zoonotic threat. This study develops a stage-structured mathematical model of leptospirosis transmission incorporating vaccine-induced immunity and two-stage treatment. The basic reproduction number , derived via the Next-Generation Matrix method, serves as a threshold where  indicates disease elimination, whereas  indicates persistence, with equilibrium stability analyzed using the Routh-Hurwitz criterion. To evaluate controls, we explicitly contrast two parameter regimes: a disease-free scenario under high interventions and reduced contact rates  resulting in , and an endemic scenario with low interventions and a high contact rate  yielding  Vaccination and awareness alone cannot eliminate the disease; reducing human-vector contact rates  through environmental control is strictly required. Combining 80% vaccination and 40% awareness with these environmental measures reduces transmission potential by 88%, providing quantifiable public health policies.
Co-Authors Dinta Ardelia Wahyudi Ega Ananta Erlangga