arXiv subjects

M. Gabriela M. Gomes

Publications and source records attributed to M. Gabriela M. Gomes.

7 recordsLinked to original sources

arXiv2026

From Individual-Based Stochastic Epidemics to Heterogeneous SIR Equations

We develop a stochastic framework for a broad class of heterogeneous SIR epidemic models. In the finite-population construction, each initially susceptible individual is assigned a fixed nonnegative susceptibility, and infection occurs when the accumulated population-level infection pressure exceeds an individual random threshold. Infectious periods are independent and exponentially distributed with a common recovery rate. For any susceptibility distribution with finite mean, we prove a uniform-on-compact law of large numbers for the susceptible, infectious, removed, and cumulative infection-pressure processes. In the limit, an individual with susceptibility lambda remains susceptible under cumulative pressure x with probability exp(-x lambda). It follows that the susceptible fraction is given by the Laplace transform of the initial susceptibility distribution, while the incidence rate is governed by the mean susceptibility among those who remain susceptible. The resulting limits recover several familiar heterogeneous SIR systems, including the classical power-law model, and also yield other closed nonlinear incidence forms. The framework therefore provides a unified probabilistic foundation for deterministic epidemic models with persistent individual heterogeneity.

math.PR↗

arXiv2026

The impact of nonheritable variation in division rates on population growth across environments

Phenotypic heterogeneity is a pervasive feature of biological populations, yet its impact on population growth is often interpreted through changes in mean individual fitness alone. In this paper, we investigate how nonheritable variability in division rates influences the asymptotic growth of a population. Using a class of linear models with phenotypic structure, we show that variability modifies the dominant eigenvalue of the system in a nonlinear manner, leading to an intrinsic tradeoff: while variability reduces population growth under favourable conditions, it mitigates population decline under stress. These results provide a simple mechanistic framework for understanding how heterogeneity influences population-level dynamics. In particular, they suggest that stress-dependent amplification of mutational effects may arise from changes in phenotypic variability, rather than from changes in mean fitness alone. We illustrate this mechanism using mutation accumulation data in Chlamydomonas reinhardtii, where the observed patterns of relative fitness under increasing stress are consistent with increased variability within genotypes. More broadly, our analysis highlights the importance of variability as a determinant of population growth, and shows that some effects commonly attributed to changes in mean fitness may instead reflect the nonlinear consequences of phenotypic heterogeneity.

q-bio.PE↗

arXiv2026

An exploration into how susceptibility distribution misspecifications impact epidemic forecasting

Heterogeneous susceptibility models for epidemic dynamics preferentially assume that individual susceptibility follows a gamma distribution, which permits analytical reduction to a low-dimensional system. However, the true empirical distributional form in any given population is unknown. Here we investigate the consequences of misspecifying the susceptibility distribution by comparing gamma and lognormal specifications in a Susceptible-Exposed-Infectious-Removed (SEIR) framework. When both distributions are matched on mean and coefficient of variation ($ν$), we find that their epidemic trajectories diverge once heterogeneity is moderate or high ($ν\gtrsim 1$), with the lognormal producing a later, larger peak and a greater final size. We then assess the impact of distributional misspecification on statistical inference. Using synthetic datasets, we fit correctly specified and misspecified models by maximum likelihood. In a default scenario, where inference is based on simulated data for a single epidemic, both models can reproduce the data by compensating through correlated shifts in heterogeneity and intervention parameters. When inference is based on two simulated epidemics, however, this compensation may be reduced by known constraints of how parameters are related across epidemics. In these cases, the correctly specified model recovers all parameters accurately, while the misspecified model tends to give biased estimates. These inference biases propagate into forecasts, but predictions remain relatively accurate when compared to homogeneous models which more than double peak incidences in scenarios where $ν\approx 1$, for instance. We conclude that deviations resulting from the susceptibility distribution misspecifications assessed here are minor and encourage the adoption of heterogeneous models in future epidemic forecasting.

stat.AP↗

arXiv2025

On the simultaneous inference of susceptibility distributions and intervention effects from epidemic curves

Susceptible-Exposed-Infectious-Recovered (SEIR) models with inter-individual variation in susceptibility or exposure to infection were proposed early in the COVID-19 pandemic as a potential element of the mathematical/statistical toolset available to policy development. In comparison with other models employed at the time, those designed to fully estimate the effects of such variation tended to predict small epidemic waves and hence require less containment to achieve the same outcomes. However, these models never made it to mainstream COVID-19 policy making due to lack of prior validation of their inference capabilities. Here we report the results of the first systematic investigation of this matter. We simulate datasets using the model with strategically chosen parameter values, and then conduct maximum likelihood estimation to assess how well we can retrieve the assumed parameter values. We identify some identifiability issues which can be overcome by creatively fitting multiple epidemics with shared parameters.

stat.AP↗

arXiv2025

A note on metapopulation models

Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of species, differentiation of populations, and persistence of infectious diseases. Here, focusing on infectious disease epidemiology, we take a complementary approach and study the effects of individual variation within patches while neglecting any form of disease transmission between patches. Consistently with previous work on single populations, we show how metapopulation models that neglect in-patch heterogeneity also underestimate basic reproduction numbers ($\mathcal{R}_{0}$) and the effort required to control or eliminate infectious diseases by uniform interventions. We then go beyond this confirmatory result and introduce a scheme to infer distributions of individual susceptibility or exposure to infection based on suitable stratifications of a population into patches. We apply the resulting metapopulation models to a simple case study of the COVID-19 pandemic.

q-bio.PE↗

arXiv2022

Unfolding selection to infer individual risk heterogeneity for optimising disease forecasts and policy development

Mathematical models are increasing adopted for setting targets for disease prevention and control. As model-informed policies are implemented, however, the inaccuracies of some forecasts become apparent, for example overprediction of infection burdens and overestimation of intervention impacts. Here, we attribute these discrepancies to methodological limitations in capturing the heterogeneities of real-world systems. The mechanisms underpinning single factors for infection and their interactions determine individual propensities to acquire disease. These are potentially so numerous that to attain a full mechanistic description may be unfeasible. To contribute constructively to the development of health policies, model developers either leave factors out (reductionism) or adopt a broader but coarse description (holism). In our view, predictive capacity requires holistic descriptions of heterogeneity which are currently underutilised in infectious disease epidemiology but common in other disciplines.

q-bio.PE↗

arXiv2022

Herd immunity under individual variation and reinfection

We study a SEIR model considered by Gomes et al. \cite{Gomes2020} and Aguas et al. \cite{Aguas2020} where different individuals are assumed to have different levels of susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We find explicit formulas to calculate herd immunity thresholds and stable configuration, and explore extensions of the model.

q-bio.PE↗