LEAPS-MPS: Incorporating Stratification by Vaccination Status and Virus Variants in Mathematical Models of Infectious Disease Spread

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).

Since the beginning of the COVID-19 pandemic, mathematical modeling has played a significant role in assessing and forecasting the impacts of the disease and guiding public health policy. Existing mathematical frameworks, however, have been slow to adapt to sudden changes in disease spread dynamics resulting from the waning vaccine immunity and emergence of COVID-19 variants such as delta and omicron. This project will address these challenges by developing data-driven mathematical modeling tools which divide populations according to factors that have distinct characteristics, such as those due to differences in vaccination status and the spread of virus variants. As COVID-19 evolves and becomes endemic in the global population, the developed frameworks will guide public health officials in evaluating the effectiveness of potential vaccination strategies and assessing the capacity of variants to alter the course of disease spread. This will facilitate targeted and impactful policies rather than disruptive population-wide restrictions and lockdowns. The project will engage undergraduate students in topical applied mathematics research and support underrepresented students in STEM with a particular focus on the African American community in Metro Detroit. The project will additionally advance curricular and program development at Lawrence Technological University, which will enhance the institution's research environment and further the principal investigator's professional goal of establishing a sustained, student-focused, and interdisciplinary research program in mathematical biology at Lawrence Technological University.

Traditional mathematical modeling frameworks of infectious disease spread often ignore factors of heterogeneous spread within a population. This can lead to poor estimates of epidemiological parameters (such as the basic reproduction number and herd immunity threshold), mistaken assessments of the mechanisms of disease spread, and inaccurate forecasts. This project will develop the theory and application of compartmental SIR-type (Susceptible-Infectious-Recovered) models, which are associated with a system of ordinary differential equations, to incorporate variances in a population's vaccination coverage level, differing waning immunity periods, and competition between virus variants with distinct epidemiological characteristics. Waning immunity will be incorporated through a gamma-distributed delay on return to susceptibility after vaccination or previous infection. The resulting distributed delay differential equations will be analyzed and numerically simulated using the linear chain trick, which reduces gamma-distributed delays to a linear chain of exponential delays. Case data from The Michigan Department of Health and Human Services will be used to parametrize and validate the models with the goal of providing insightful forecasts for the spread of COVID-19 under different immunization schedules. Virus variants will be incorporated by dividing the infectious class into distinct compartments with variant-specific parameters, such as variances in transmissibility, severity, vaccine resistance, reinfection rate, and diagnostic detection. The goal will be to establish novel critical thresholds for when a virus variant can persist or become dominant in a population as well as address the inverse question of estimating a variant's epidemiological parameters from its early-stage growth. By controlling a population's vaccination coverage level, the developed models will be able to cut through the complexity of case incidence data to provide critical insights into the primary factors driving disease spread. User-friendly computational packages capable of implementing the models and interfacing with public health databases will be developed.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.