Modelling Leptospirosis Transmission with Waning Immunity and Stage-Structured Infection: Local stability and Vaccination Analysis - Dinta Ardelia Wahyudi; Budi Priyo Prawoto (UIN Sumatera Utara, 2026)
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.