Recent advances in Epidemic theory

Nir Gavish

Technion Israel Institute of Technology

"Optimal vaccination for contagious diseases with seasonal transmission"

We consider epidemiological models with seasonality and ask what the optimal temporal vaccination profile is that minimizes the basic reproduction number defined over a season, given a constraint on the total annual number of vaccinations. We do not impose any a priori assumptions about the structure or regularity of the optimal vaccination profile. In particular, we allow the vaccination profile to include delta functions corresponding to pulse vaccination. To do so, we consider a periodic optimal control problem over a measure space. Using non-standard tools that do not rely on Pontryagin's theorem for optimal control problems, we characterize the solution to the problem. In addition, we develop an efficient numerical scheme for computing the optimal vaccination profile over time. This is a joint work with Guy Katriel

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Amit Huppert

Tel Aviv University

"Modeling Predation in Bacterial Interactions"

We developed a mathematical model to explore density-dependent predation in microbial systems. Density dependence is a fundamental ecological mechanism that influences population dynamics and regulation. While mathematical modeling is a valuable tool for quantifying predator-prey interactions, a research gap exists in exploring the nature of predator growth's dependence on prey density through a combination of empirical and mathematical approaches within the prey-predator framework. We developed mathematical ODE models and fitted them to experimental time-series data from microbial predator-prey systems. These models incorporated different functional responses—specifically Holling types I, II, and III—which describe the relationship between prey density and predator foraging. Parameter inference was performed using a Bayesian approach with the Markov Chain Monte Carlo (MCMC) technique, adapting the framework to handle multi-replicate time-series data. We employed two distinct modeling approaches: Single Interval Modeling, which fits one model to the entire dataset, and Phased Interval Modeling, which divides the 96-hour period into three distinct phases (0-12, 12-48, and 48-96 hours) and fits separate models to each. Model selection in both approaches was based on likelihoods, AIC, and BIC. The study revealed distinct dynamics in each phase. In Phase I, the predator's per-capita growth rate (PGR) was density independent, and a simple model assuming the predator's total time was spent handling prey provided a good fit with an analytical solution. Phase II exhibited density-dependent dynamics, where the predator's PGR changed with prey density; the best model for this phase was an ODE model with a Holling type-III functional response. In Phase III, following prey depletion, the predator population showed exponential death, and its PGR was again density independent.

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Byul Nim Kim

Kyung Hee University

"Empirical and Spatiotemporal Approaches to Effective Reproduction Number Estimation: Insights from Network and Mobility Models in South Korea"

Understanding the effective reproduction number (R_t) is crucial for real-time epidemic assessment and public health intervention. This presentation introduces and synthesizes three advanced approaches for estimating Rt during the COVID-19 pandemic in South Korea, highlighting their methodological innovations and practical implications. First, the Transmission Potential (TP) model integrates household vs. non-household transmission, mobility patterns (via Google data), and social distancing behaviors to estimate Reff in real time. By distinguishing the impact of mobility changes on different transmission settings, this model provides dynamic and context-aware Reff estimates, outperforming conventional methods like Cori's Rt in sensitivity and short-term prediction​. Second, an empirical infection network-based R_t model uses real-world infector-infectee pair data to directly compute R_t without relying on assumptions of homogeneous mixing. This network approach captures the heterogeneity of regional and demographic transmission, especially during superspreading events and early epidemic phases, where traditional models often underperform​. Third, a multi-patch SEIIR model with mobility-informed regional Reff quantifies both local and interregional transmission. Using high-resolution mobility data and compartmental modeling across 17 regions, it reveals Seoul and Gyeonggi as dominant transmission hubs. The study emphasizes phase-specific and region-targeted mobility interventions as more effective than uniform national policies​. Together, these studies highlight the need for adaptive, data-driven R_t estimation frameworks that incorporate real-time behavior, mobility, and infection network structures. The integration of these methods advances epidemic modeling and supports refined public health strategies tailored to regional and temporal dynamics.

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Kyeongah Nah

National Institute for Mathematical Sciences

"Age-structured modeling of tuberculosis in South Korea and insights for national control strategies"

Despite improvements in its national tuberculosis (TB) control program and rapid economic growth, South Korea continues to report the highest TB incidence among OECD countries. Addressing this challenge requires an understanding of the changing trends of TB burden across different age groups and a long-term evaluation of policies aimed at TB control. This study introduces an age-structured population dynamics to analyze the dynamics of TB transmission under national control in Korea. We perform retrospective assessments and future projections to assess the impact of Public-Private Mix (PPM) strategies on TB incidence. Additionally, we explore how this model could be extended to provide insights for designing effective TB control policies.

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