Postdoctoral Research at the University of Notre Dame, Indiana (Jan 2022 - Aug 2023)

I worked at the Perkins lab in the Department of Biological Sciences and conducted research related to estimating optimal controls of vaccination and control measures of the mosquito-borne disease, Dengue. 

Dengue is one of the most common mosquito-borne diseases in the world, and a person can get infected by one of the four serotypes of the virus named DENV-1, DENV-2, DENV-3, and DENV-4. After infection with one of these serotypes, an individual will maintain permanent immunity to that serotype, and partial immunity to the other three serotypes. Therefore, there is a risk of getting infected by this virus a maximum of four times, and the symptoms may vary from mild fever to high fever, bleeding, enlarged liver, and severe shock, and sometimes these symptoms may lead to death. It is obvious that the increase in the number of infected individuals makes a negative impact on a country’s economy. Hence, the use of different control measures such as mosquito repellents and the introduction of a vaccine against the virus is important in controlling the spread of the virus. In this work, I studied the methodologies on how to estimate the optimal rate of vaccinations based on the QDENGA dengue vaccine and the optimal rate of control measures to reduce the number of new and severe dengue cases while minimizing the overall cost. Even though this vaccine claimed high protection against symptomatic disease and waning protection over time for some DENV serotypes, the extent to which protection against disease conditional on infection was unknown. I considered different scenarios subject to the possible combinations of vaccine protection and control measures to investigate the most effective parameter values to control the transmission of the virus. Disease forecasts including the number of newly infected individuals in each serotype, the optimal rate of control measure, and vaccinations for a period of ten years were performed with the help of computer software.

Postdoctoral Research at Northern Arizona University, Arizona (Jan 2021 - Jan 2022)

During this NSF-funded research project, I studied the transmission of the SARS-CoV-2 pathogen in regional, rural networks in Arizona under the supervision of Dr. Mihaljevic at the School of Informatics, Computing, and Cyber Systems. My contributions to this project can be divided into two main categories; they are forecasting county-level COVID-19 projections in Arizona and time-varying parameter estimation of a COVID-19 model (https://sparsemod.nau.edu/ ).

In the first phase of the project, county-level projections were made for new and total numbers of asymptomatic cases, presymptomatic cases, hospitalizations, deaths, etc. using our group-written SPARSEMODr R-package, which is written based on mathematical modeling of infectious diseases and statistical techniques. The results were shared regularly with researchers from other universities in Arizona (UOA, ASU) and with health officials from the Arizona Department of Health Services (AZDHS).

During the second phase, a computer algorithm was constructed using statistical tools and C++ language to estimate the time-varying parameters of a spatially explicit and stochastic covid-19 model. In my method, I mainly focused on optimizing SARS-COV-2 transmission rates and host movement rates. I introduced a user-friendly algorithm using the grid search method and the sliding window technique. The algorithm can be implemented efficiently on a high-performance computing cluster. I showed that the method can estimate time-varying transmission rates with high accuracy and precision and movement rates with lower precision. The summary of the method and results were published in PLOS Global Public Health Journal.

Graduate Research at Texas Tech University, Texas (Aug 2014 - Aug 2019)

In my work, I introduced and analyzed different approaches to overcome some issues in computing fractional Sobolev norms in the context of PDE-constrained boundary optimal control problems with Dirichlet control. Dirichlet boundary optimal control problems are perhaps the most interesting class of optimal control problems constrained by partial differential equations (PDEs). In fact, the possibility of controlling the behavior of a physical system may often take place only by changing the values of certain quantities at the boundary of the domain, especially when the interior of the physical system is not accessible and when no physical mechanism can be triggered inside the domain from the outside. 

The first approach that was considered in this work keeps the control function on the boundary by replacing fractional norms with integer norms. This approach is a simple way to overcome the need of explicitly computing fractional norms. Then, two other approaches were proposed that make use of the lifting functions of the boundary controls. These lifting functions become a new class of control functions in the statement of the optimal control problem. They can be chosen to be defined either inside the original domain of the state problem or outside of it. I compared these two lifting approaches with the first approach on the boundary. 

Another goal of this research was to add control inequality constraints to all the above approaches. In order to deal with these, the Primal-Dual Active Set method was used. The optimality systems arising from first-order necessary conditions were discretized using the finite element method. Numerical results were presented to compare the convergence rate, computational cost, and accuracy of each optimal control problem.