DE Seminar: Undergraduate Student Presentations

Speaker 1: Owen McMann

Identifiability, Reproduction Number, and Stability

Analysis

Abstract: We analyze a normalized compartmental model for dengue transmission in which x is the fraction of susceptible humans, y the fraction of infected humans, and z the fraction of infected mosquitoes. The reduced three–ODE system is obtained from an original five–equation host–vector model by assuming constant total human and mosquito populations and normalizing each compartment. The system admits two biologically relevant equilibria: a disease-free equilibrium (DFE) and an endemic equilibrium. We derive the basic reproduction number R0 and show it governs a bifurcation between the two regimes. For R0 < 1 we construct an explicit Lyapunov function and prove nonlinear local asymptotic stability of the DFE under the normalized dynamics. For R0 > 1 linearization about the endemic equilibrium combined with the Routh–Hurwitz criterion establishes local asymptotic stability. To assess the ability to estimate the parameters of the model, we perform structural identifiability analysis with two independent symbolic tools, DAISY and SIAN, which corroborate global (structural) identifiability of the normalized model. Building on these theoretical results, we implement a data-assimilation pipeline using nudging to incorporate noisy observations and constrain trajectories; parameter estimation will fit the model to synthetic and empirical datasets. The combined stability and identifiability evidence supports the model’s use for evaluating targeted control strategies (e.g., reducing transmission rates or vector abundance) in realistic outbreak scenarios.

Title: TBD