Research Highlights

Mathematical Modeling of Infectious Diseases

Mathematical models can be useful for modeling and analyzing infectious diseases and illness transmission among groups or within one host.   Prof. Fathalla Rihan's research group developed differential equations to model infectious diseases and conditions to control them.  Springer published his book "Delay Differential Equations with Applications to Biology" in 2021. There are 14 chapters in this book that discuss delay differential equations and their applications in biosciences. The book presents a wide class of delay differential equations with integer and fractional-order derivatives for the analysis of dynamical and biological systems, which provide a richer mathematical framework than differential equations without memory. There are also interesting applications of delay differential equations to immunology and infectious diseases, including COVID-19, and tumor-immune interactions.  The book is valuable to graduate and undergraduate mathematicians, and specialists in the fields of mathematical biology, mathematical modeling, life sciences, optimal control, immunology, and infectious diseases. It also bridges the mathematical and biological communities.

In the UAE, we have proposed a class of stochastic COVID-19 epidemic models. Environmental factors, such as humidity, precipitation, temperature, and awareness of people, influence the spread of the new strain of Coronavirus COVID-19 to humans.  Time delays and cross-immune status (people who have recovered from infection by different strains of the same subtype in previous years) were studied in transmission terms for COVID-19 spread.  Several sufficient conditions for disease persistence and extinction were established. Due to the presence of time-delay (memory) in the transmission terms, outbreaks can be periodic. Susceptible-Infected-Asymptomatic-Quarantined-Recovered (SIAQR) is also modeled stochastically in the UAEU.

In modeling COVID-19, the following articles/results were most interesting:

• Stochastic SIRC Epidemic Model with Time- Delay for COVID-19. Advances in Difference Equations, 2020, 502 (2020).
• Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE, Results in Physics, Volume 28, September 2021, 104658.
• Dynamics of a Stochastic Epidemic Model with Vaccination and Multiple Time-Delays for COVID-19 in the UAE, Complexity, 2022, 4247800;
• A fractional-order model with different strains of COVID-19, Physica A, 603 (2022) 127813.
• Immunokinetic Model for COVID-19 Patients, Complexity, Volume 2022, Article ID 8321848.
• Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination. Nonlinear Dynamics (2021).
• Dynamics and Sensitivity of Fractional-Order Delay Differential Model for Coronavirus (COVID-19) Infection, Progress in Fractional Differentiation and Applications, 7 (1) 2021, 43–61.

Research teams from UAEU, Zayed University, and other universities outside the country collaborate on some running projects:

• ZU-UAEU Project, ”Impact of Stochastic Noise on COVID-19 Dynamics in the UAE: Analysis, control, and treatment”.
• SURE+ 2022 program, “Mathematical Modeling of COVID-19 infection in the UAE”.
• UPAR-UAEU Project, ”Quantitative and Quantitative Features of Delay Differential Equations With Infectious Diseases”.
• PhD Project, “Mathematical Modeling of Immune System-Tumor Cell Growth Interactions Mathematical Modeling of Immune System - Tumor Cell Growth Interactions”.
• PhD Project, “Stochastic Delay Differential Equations with Applications in Ecology and Epidemics".

The Department of Mathematical Sciences is one of the top research departments at the university and even in the country. There are strong research groups in both applied and pure mathematics in the department. It also has a number of distinguished professors with doctorates in science.