Stability and Sensitivity Analysis of a Logistic SEIR Model for Vector-Borne Epidemic Disease

Abstract

A SEIR model with logistic carrying capacity has previously been used to describe dengue infection dynamics, with stability established at a single fixed parameter set via Routh-Hurwitz analysis of the model's Jacobian. This paper extends that single-point stability result into a full sensitivity and stability landscape: a one-at-a-time normalized sensitivity analysis identifies which of the model's seven parameters most strongly influence peak infection severity, and a two-dimensional numerical eigenvalue sweep over carrying capacity K and transmission rate β traces the stability boundary separating locally stable and unstable regimes. The results show that peak infection is most sensitive to carrying capacity K and transmission rate β (both with normalized sensitivity indices above 1.2), and that the stability boundary in (K, β) space is a hyperbola-like curve, such that stability requires either high carrying capacity paired with low transmission, or the reverse — a trade-off not evident from the single-parameter-set analysis in the original model.