Mathematical Modeling and Computing to Study the Influence of Quarantine Levels and Common Mitigation Strategies on the Spread of COVID-19 on a Higher Education Campus

In this work, we develop a mathematical model to study the COVID-19 dynamics on a higher education campus. The proposed model builds on successful compartmental models that describe the dynamics of the spread of disease between multiple student sub-populations within a closed environment. The model assumes no vaccinations and includes three different levels of quarantine adherence to represent student behavior with the common mitigation strategies of face mask usage and random testing. A detailed analysis of the model including boundedness and positivity of the solutions along with a derivation of the basic reproduction number for the model is presented. Additionally, we also create an interactive graphical user interface through a dashboard for public use. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Computational modeling, analysis and simulation for lockdown dynamics of COVID-19 and domestic violence

As potential strategies to control the spread of COVID-19, governments all across the globe have implemented interventions such as lockdowns and confinement. While these strategies have helped to control the spread, there have also been evidence of widespread increase in Domestic Violence (DV) which is often under-reported. In this work, we have developed two new models that will help study the relationship between lockdowns, the spread of COVID-19 and DV in the hope of mitigating the social problems that follow such drastic measures. Two different models, in increasing level of complexity have been employed to simulate the effect of the lockdown strategy in the spread of COVID-19 and DV. One of the models simulates the spread of DV under three different lockdown scenarios: one long period, two and three shorter intervals that comprise the same interval of time since onset of the Pandemic. Another model studies the interaction between COVID-19 and DV during confinement in relation to the length of the lockdowns. Our findings indicate multiple lockdowns are safer for DV but not necessarily for controlling spread of COVID-19. We also present a derivation of the basic reproduction number for the model involving the interaction between COVID-19 and DV. © 2022

Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction

In this work, the dynamics of the spread of COVID-19 is considered in the presence of both human-to-human transmission as well as environment-to-human transmission. Specifically, we expand and modify traditional epidemiological model for COVID-19 by incorporating a compartment to study the dynamics of pathogen concentration in the environmental reservoir, for instance concentration of droplets in closed spaces. We perform a mathematical analysis for the model proposed including an endemic equilibrium analysis as well as a next-generation approach both of which help to derive the basic reproduction number. We also study the efficacy of wearing a facemask through this model. Another important contribution of this work is the introduction to physics informed deep learning methods (PINNs) to study the dynamics. We propose this as an alternative to traditional numerical methods for solving system of differential equations used to describe dynamics of infectious diseases. Our results show that the proposed PINNs approach is a reliable candidate for both solving such systems and for helping identify important parameters that control the disease dynamics. © 2022 Long Nguyen et al., published by De Gruyter.

Mathematical modeling, analysis, and simulation of the COVID-19 pandemic with explicit and implicit behavioral changes

As COVID-19 cases continue to rise globally, many researchers have developed mathematical models to help capture the dynamics of the spread of COVID-19. Specifically, the compartmental SEIR model and its variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. Yet, while the spread of COVID-19 is largely attributed to a wide range of social behaviors in the population, several of these SEIR models do not account for such behaviors. In this project, we consider novel SEIR-based models that incorporate various behaviors. We created a baseline model and explored incorporating both explicit and implicit behavioral changes. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of secondary cases by a single infected individual. Numerical simulations for the various models we made were performed and user-friendly graphical user interfaces were created. In the future, we plan to expand our project to account for the use of face masks, age-based behaviors and transmission rates, and mixing patterns. © 2020 Comfort Ohajunwa et al., published by De Gruyter.