BASIC REPRODUCTION NUMBER OF A VARICELLA SVEIR MODEL WITH IMPERFECT TWO-DOSE VACCINATION
Keywords:
varicella, SVEIR model, vaccination, basic reproduction number, next-generation matrix, stabilityAbstract
Varicella (chickenpox) remains a public health concern even where vaccination is routine. We propose a deterministic SVEIR model that includes newborn vaccination, vaccination of susceptible individuals, imperfect vaccine protection, waning of first-dose immunity, and a second dose assumed to confer permanent immunity. Using the next-generation matrix method we obtain a closed-form expression for the basic reproduction number R₀ and show that the disease-free equilibrium is locally asymptotically stable if R₀ < 1 and unstable if R₀ > 1. The formula expresses R₀ as the unvaccinated baseline multiplied by a vaccination reduction factor, which is non-increasing in every vaccination parameter. Illustrative calculations with hypothetical parameters indicate that adding the second dose yields a smaller reduction factor in the selected scenarios.
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