arXiv subjects

Necibe Tuncer

Publications and source records attributed to Necibe Tuncer.

5 recordsLinked to original sources

arXiv2026

A Tutorial on Structural Identifiability of Epidemic Models Using StructuralIdentifiability.jl

Structural identifiability is the theoretical ability to uniquely recover model parameters from ideal, noise-free data and is a prerequisite for reliable parameter estimation in epidemic modeling. Despite its importance for calibration and inference, structural identifiability analysis remains underused and inconsistently applied in infectious disease modeling. This paper presents a user-oriented methodological tutorial demonstrating how global structural identifiability analysis can be systematically integrated into epidemic modeling workflows. We provide a reproducible framework for conducting structural identifiability analysis of ordinary differential equation models using the Julia package StructuralIdentifiability.jl. The workflow is illustrated across commonly used epidemic models, including SEIR variants with asymptomatic and presymptomatic transmission, vector-borne disease models, and systems incorporating hospitalization and disease-induced mortality. We also introduce a visual communication strategy that embeds identifiability results directly into compartmental diagrams, facilitating interpretation and interdisciplinary communication. Our results show that identifiability depends critically on model structure, the choice of observed variables, and assumptions about initial conditions, and that identifiable parameter combinations may exist even when individual parameters are not globally identifiable. Emphasizing transparent implementation, interpretation, and communication, this work provides practical guidance and comparative insights across model classes. The tutorial is designed as both a reference and a teaching resource for researchers and educators seeking to incorporate structural identifiability analysis into epidemic model development. All code and annotated diagrams are publicly available to ensure reproducibility and reuse.

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arXiv2025

Structural and Practical Identifiability of Phenomenological Growth Models for Epidemic Forecasting

Phenomenological models are highly effective tools for forecasting disease dynamics using real world data, particularly in scenarios where detailed knowledge of disease mechanisms is limited. However, their reliability depends on the model parameters' structural and practical identifiability. In this study, we systematically analyze the identifiability of six commonly used growth models in epidemiology:the generalized growth model, the generalized logistic model, the Richards model, the generalized Richards model, the Gompertz model, and a modified SEIR model with inhomogeneous mixing. To address challenges posed by non-integer power exponents in these models, we reformulate them by introducing additional state variables. This enables rigorous structural identifiability analysis using the StructuralIdentifiability.jl package in JULIA. We validate the structural identifiability results by performing parameter estimation and forecasting using the GrowthPredict MATLAB toolbox. This toolbox is designed to fit and forecast time series trajectories based on phenomenological growth models. We applied it to three epidemiological datasets: weekly incidence data for monkeypox, COVID 19, and Ebola. Additionally, we assess practical identifiability through Monte Carlo simulations to evaluate parameter estimation robustness under varying levels of observational noise. Our results confirm that all six models are structurally identifiable under the proposed reformulation. Furthermore, practical identifiability analyses demonstrate that parameter estimates remain robust across different noise levels, though sensitivity varies by model and dataset. These findings provide critical insights into the strengths and limitations of phenomenological models to characterize epidemic trajectories, emphasizing their adaptability to real world challenges and their role in informing public health interventions.

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arXiv2023

Structural identifiability analysis of epidemic models based on differential equations: A tutorial-based primer

The successful application of epidemic models hinges on our ability to estimate model parameters from limited observations reliably. An often-overlooked step before estimating model parameters consists of ensuring that the model parameters are structurally identifiable from the observed states of the system. In this tutorial-based primer, intended for a diverse audience, including students training in dynamic systems, we review and provide detailed guidance for conducting structural identifiability analysis of differential equation epidemic models based on a differential algebra approach using DAISY (Differential Algebra for Identifiability of SYstems) and \textit{Mathematica} (Wolfram Research). This approach aims to uncover any existing parameter correlations that preclude their estimation from the observed variables. We demonstrate this approach through examples, including tutorial videos of compartmental epidemic models previously employed to study transmission dynamics and control. We show that the lack of structural identifiability may be remedied by incorporating additional observations from different model states, assuming that the system's initial conditions are known, using prior information to fix some parameters involved in parameter correlations, or modifying the model based on existing parameter correlations. We also underscore how the results of structural identifiability analysis can help enrich compartmental diagrams of differential-equation models by indicating the observed state variables and the results of the structural identifiability analysis.

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arXiv2022

Finite Element Approximation of Invariant Manifolds by the Parameterization Method

We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium solutions of nonlinear parabolic PDEs. The parameterization method provides an infinitesimal invariance equation for the invariant manifold, which we solve via a power series ansatz. A power matching argument leads to a recursive system of linear elliptic PDEs -- the so-called homological equations -- whose solutions are the power series coefficients of the parameterization. The homological equations are solved recursively to any desired order using finite element approximation. The end result is a polynomial expansion for a chart map of the manifold, with coefficients in an appropriate finite element space. We implement the method for a variety of example problems having both polynomial and non-polynomial nonlinearities, on non-convex two-dimensional polygonal domains (not necessary simply connected), for equilibrium solutions with Morse indices one and two. We implement a-posteriori error indicators which provide numerical evidence in support of the claim that the manifolds are computed accurately.

math.DS↗

arXiv2021

Sensitivity analysis in an Immuno-Epidemiological Vector-Host Model

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease (RFVD) utilizing parameter estimations from prior studies. SA indicates that 1% increase in within-host pathogen growth rate can lead up to 8% increase in R0; up to 1% increase in steady-state infected host abundance, and up to 4% increase in infectiousness of hosts when the reproduction number R0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

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