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

Dinta Ardelia Wahyudi, Budi Priyo Prawoto

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.

Keywords


Basic reproduction number; Leptospirosis; Routh-Hurwitz; Stage-structured model; Vaccination.

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DOI: http://dx.doi.org/10.30829/zero.v10i2.30511

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