Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

Modelling Leptospirosis Transmission with Waning Immunity and Stage-Structured Infection: Local stability and Vaccination Analysis

Dinta Ardelia Wahyudi (Department of Mathematics, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia)
Budi Priyo Prawoto (Department of Mathematics, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia)



Article Info

Publish Date
29 Jul 2026

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.

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