Ibrahim H. Aslan



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  •   Summary of Research
My research area is applied mathematics. More precisely, I am interested in mathematical modeling of biological systems, statistical modeling, scientific computing, optimal control theory, differential equations and stochastic optimization. I have been studying on various statistical and mathematical models to understand the behavior of biological structures and I have developed mathematical models for an epidemiological disease Leptospirosis.

One of my study is a stochastic optimization model for cost effectiveness analysis in early detection of Leptospirosis. I have been seeking an optimal treatment strategy for the patients coming into a hospital with the symptoms similar to the symptoms of Leptospirosis. I have developed a stochastic processing model into a computational algorithm to compare treatment strategies and determine the optimal management strategy maximizing the number of early detected Leptospirosis cases and minimizing the corresponding cost.

My current work is a mathematical model of Leptospirosis with impulse actions in cattle. I am interested in understanding the propagation of Leptospirosis and finding a schedule of control programs to eradicate the disease in a cattle ranch. The model has been built with ordinary differential equations (ODEs) and included some vaccination and recruitment control programs in the form of impulse actions to prevent the propagation of Leptospirosis in the cattle ranch. This system of ODEs with impulse actions determines a schedule of control actions in order to eradicate Leptospirosis in the ranch. Parameter estimation and sensitivity analysis were completed for the model.

I have been working on varied statistical models, statistical learning methods and the concepts for supervised and unsupervised learning in a course framework. I have studied model selection, support vector machines, kernel methods, clustering, boosting and ensem- ble learning. I performed statistical learning methods to build predictive models and tuned these statistical learning methods correctly to assess model fit and error.

                                                                  
     Last update 11/14/2018