Mathematical Epidemiology 

The rising number of novel pathogens threatening the human population has motivated the application of mathematical modeling for forecasting the trajectory and size of epidemics. Since epidemics associated with infectious diseases of rapid dissemination typically comprise only a few disease generations of transmission, epidemic assessment using forecasting models is crucial during the early epidemic growth phase. In order to assess the potential disease burden posed by the infectious agent and approximate the scale of interventions needed to achieve epidemic containment, development of disease forecasting models are necessary.

My research in this area builds upon the modeling work of researchers interested in developing and testing a family of “first response” models that can be quickly calibrated to estimate disease burden. My collaborators and I have used simple phenomenological models during the recent Ebola epidemic, Zika Virus outbreak in Antioquia, Colombia and the 2015 Ebola Challenge to provide estimations of epidemic burden and characterize the basic reproduction number. The use of simple phenomenological models has also led to findings of sub-exponential epidemic growth in a diverse set of diseases. This has motivated the mathematical development and analysis of mechanistic models that incorporate sub-exponential epidemic growth. These simple phenomenological models have also yielded a tractable way of analyzing how migration can change the final epidemic size. 

Relevant Research Articles

M. D Johnston, B. Pell, P. Nelson. A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia. Applied Sciences. 2022; 12(3):1723. https://doi.org/10.3390/app12031723

M. D. Johnston and B. Pell. A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread. Mathematical Biosciences and Engineering 17 (6): 7892-7915, 2020. 

B. Pell, T. Phan, E. M. Rutter, G. Chowell, & Y. Kuang. Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay Mathematical Biosciences, 2018, 301, 83 – 92. 

B. Pell, Y. Kuang, C. Viboud, &amp G. Chowell. Using phenomenological models for forecasting the 2015 Ebola challenge. Epidemics, 2018, 22, 62 – 70. 

G. Chowell, D. Hincapie-Palacio, J. Ospina, et al. Using Phenomenological Models to Characterize Transmissibility and Forecast Patterns and Final Burden of Zika Epidemics. PLoS Curr. 2016. 

D. J. Coffield Jr, A. M. Spagnuolo, M. Shillor, et al. A model for Chagas disease with oral and congenital transmission. PLoS One. 2013. 

 Wastewater-based mathematical modeling serves as an indispensable tool within the field of epidemiology, offering insights into the dynamics of disease spread and aiding in public health decision-making. This approach utilizes mathematical models and computational techniques to simulate and study the transmission of diseases within populations. Here's a more detailed explanation:

Transmission Dynamics Analysis:

• • Mathematical models are used to represent the spread of infectious diseases, including viruses, bacteria, and parasites.

  • These models incorporate parameters such as disease transmission rates, incubation periods, and contact patterns to describe how infections move through a population.

  • By examining the interactions between infected and susceptible individuals, researchers can predict the course of an outbreak, including the potential for exponential growth, peak infection rates, and the impact of interventions like vaccination or social distancing.

Evaluating Control Strategies:

• • Mathematical modeling allows epidemiologists and public health officials to assess the effectiveness of various disease control measures.

  • Simulations can explore scenarios with different levels of intervention, helping to determine the best strategies for containment, mitigation, and resource allocation.

  • This information is invaluable for policymakers and healthcare professionals in planning and responding to outbreaks.

Predicting Future Trends:

• • Wastewater-based modeling is particularly relevant in the context of emerging infectious diseases or pandemics.

  • By analyzing data from wastewater samples, epidemiologists can estimate the prevalence of a disease in a community, even before clinical cases are reported.

  • These early warnings can facilitate proactive measures to limit disease spread and protect public health.

Population-Level Insights:

• • Mathematical models allow researchers to study disease dynamics at a population level, accounting for demographic factors, geographic distribution, and varying levels of immunity.

  • This provides a holistic view of disease transmission that goes beyond individual case studies.

Data Integration:

• • Integrating real-time data, such as case counts, hospital admissions, and genetic sequencing, with mathematical models enhances their accuracy and relevance.

  • These data-driven models enable rapid adaptation to evolving situations, such as the emergence of new variants or changes in public behavior.

Public Health Preparedness:

• • Wastewater-based mathematical modeling is a crucial component of pandemic preparedness efforts.

  • It helps authorities anticipate the trajectory of diseases, allocate resources, and develop proactive strategies to minimize the impact on public health.

Relevant Research Articles:

T. Phan, S. Brozak, B. Pell, J. Oghuan, A. Gitter, T. Hu, R. M. Ribeiro, R. Ke, K. D. Mena, A. S. Perelson, Y. Kuang, F. Wu, 2023. Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks, Water Research, Volume 243,120372, ISSN 0043-1354, https://doi.org/10.1016/j.watres.2023.120372.

B. Pell, S. Brozak, T. Phan, F. Wu, Y. Kuang. 2023. The emergence of a virus variant: dynamics of a competition model with cross-immunity time-delay validated by wastewater surveillance data for COVID-19. J. Math. Biol., 86, 63. https://doi.org/10.1007/s00285-023-01900-0. https://rdcu.be/c8IsW

T. Phan, S. Brozak, B. Pell, A. Gitter, A Xiao, K. D. Mena, Y. Kuang, F. Wu, 2022. A simple SEIR-V model to estimate COVID-19 prevalence and predict SARS-1 CoV-2 transmission using wastewater-based surveillance data. Science of the Total Environment. https://doi.org/10.1016/j.scitotenv.2022.159326