CSUF News Service
June 11, 2020
What is a Math Model?
Math modeling is a way of utilizing data and abstraction, or mathematical expressions, for the identification and characterization of some of the most important features associated with certain natural or experimental phenomena, such as infectious diseases.
Mathematical models can be useful for prediction — if they are built based on reliable tools and methodologies. “They may provide decision-makers with a somewhat accurate glimpse of the future,” said Sam Behseta, professor of mathematics and director of the Center for the Computational and Applied Mathematics.
However, no math model can be perfect, since they are constructed based on data and existing experiences and knowledge.
“In the case of COVID-19, if a vaccine is discovered or administered tomorrow morning, it will essentially shatter most of the existing predictive models, even the ones that are used by the Centers for Disease Control and Prevention and other governmental entities,” Behseta said.
For more information about the center and COVID-19 resources, visit the website.
While health and science researchers worldwide are racing to find a cure for COVID-19, Cal State Fullerton mathematicians are stepping up to do their part using the power of math modeling.
Sam Behseta and Derdei Bichara of the Center for Computational and Applied Mathematics teamed up to apply mathematical and statistical approaches to understand the spread and control of COVID-19 — and even the prediction of a second outbreak of the novel coronavirus.
“Many existing math models solely utilize data within each community for predicting the number of infections and fatalities in the future,” said Behseta, a statistician and professor of mathematics, who also directs the center.
“But these models fall short in exploring scenarios for the prevalence of the disease when the restrictions in multiple states are relaxed, and when populations within those states don’t follow the social distancing and self-protection guidelines.”
Behseta and Bichara, assistant professor of mathematics whose research focuses on mathematical modeling of infectious diseases, are working on creating a new math approach for the coronavirus to gauge the effects of human behavior and mobility restrictions on the spread of the deadly disease.
“Information is one of the main weapons in fighting the disease. I hope, when it comes down to devising policies that affect all of us, our work can be useful for more informative decision-making,” Behseta said. “Dr. Bichara and I have been in this game long enough to know that no single model, or group of models for that matter, will be sufficient to fully describe the ins and outs of a pandemic of this magnitude.”
Historically, the two cultures of mathematical and statistical modeling have been detached in the context of modeling contagious diseases, Bichara explained.
“This work we’re doing brings the two realms together. The main goal, broadly speaking, is to provide decision-makers and the scientific community with yet another layer of useful information as far as understanding the dynamics of COVID-19,” Bichara said.
While their research efforts are in the early stages, the mathematicians point to the massive amount of data accumulated from pandemic records across the globe that will aid them in their work. Additionally, the center has created a COVID-19 resources website, which includes the best expert models, research by faculty from CSUF and other universities, and raw data from the U.S. and other countries.
“The information on the website can be utilized as a teaching tool for years to come,” Behseta said.
This is a simulated cloud of data using a simple mathematical model.
Applying Mathematical and Statistical Approaches
Behseta’s expertise in statistics includes building statistical models for biological studies. He has worked on developing models for the patterns of nerve cells in the brain and understanding the effects of temperature and soil moisture on respiratory diseases in Central California.
Bichara has published numerous research papers on the dynamics of diseases and viruses, including malaria, tuberculosis, and Ebola, Zika and HIV. His work takes into account the effects of mobility and interaction among communities, as well as the role of human behavior in the spread of the disease.
Long before the outbreak of the coronavirus, Bichara developed what he calls “exogenous and endogenous” parameters on the speed in which a disease can spread. In other words, with the current pandemic, exogenous variables are state-imposed restrictions, such as quarantine or shelter-in-place policies, and endogenous or self-imposed restrictions deal with an individual's behavioral patterns with respect to social distancing or wearing masks in public.
“We are interested in how mobility and intrinsic human behavior alter or mitigate the spread of COVID-19 in our communities. As the pandemic sprung across the nation, many states issued shelter-in-place or lockdown policies, thereby limiting, and thus decreasing, the mobility of individuals in those states or counties. These are exogenous measures,” Bichara said.
“However, as states have started to open up for business, health officials have recommended wearing masks, observing social distancing and other such measures. These are what we refer to as endogenous measures because the responsibility falls on individuals to pursue them.”
Ultimately, the mathematicians’ goal is to assess the effectiveness of these endogenous and exogenous measures in reducing the level of COVID-19 disease incidences.
“This will eventually contribute to a better understanding of the dynamics of the disease, as well as a clearer prediction or forecast of the future trends,” Bichara said.
Contact: Debra Cano Ramos, firstname.lastname@example.org