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Öğe Forecasting and analyzing the dynamics of the outbreak in Hubei and Turkey(Bilim Akademisi, 2020) Aslan, İbrahim Halil; Demir, Mahir; Wise, Michael Morgan; Lenhart, SuzanneAs the pandemic of Coronavirus Disease 2019 (COVID-19) rages throughout the world, accurate modeling of the dynamics thereof is essential. However, since the availability and quality of data varies dramatically from region to region, accurate modeling directly from a global perspective is difficult, if not altogether impossible. Nevertheless, via local data collected by certain regions, it is possible to develop accurate local prediction tools, which may be coupled to develop global models. In this study, we analyze the dynamics of local outbreaks of COVID-19 via a coupled system of ordinary differential equations (ODEs). Utilizing the large amount of data available from the ebbing outbreak in Hubei, China as a testbed, we estimate the basic reproductive number, R0 of COVID-19 and predict the total cases, total deaths, and other features of the Hubei outbreak with a high level of accuracy. Through numerical experiments, we observe the effects of quarantine, social distancing, and COVID-19 testing on the dynamics of the outbreak. Using knowledge gleaned from the Hubei outbreak, we apply our model to analyze the dynamics of outbreak in Turkey. We provide forecasts for the peak of the outbreak and the total number of cases/deaths in Turkey, for varying levels of social distancing, quarantine, and COVID-19 testingÖğe A mathematical model for cost-effectiveness analysis and early detection of leptospirosis in human(2020-12-21) Aslan, İbrahim Halil; Lenhart, SuzanneIn this study, we developed a computational algorithm under stochasticity by using Markov-cycle tree and Monte Carlo simulations for patients coming into a hospital and being suspected of leptospirosis. Our mathematical model finds an optimal treatment strategy for the patients depending on whether they have severe or mild symptoms and whether they are late case patients who are coming to the hospital after seven days of onset of their symptoms or early case patients who are coming to the hospital within seven days of onset of their symptoms. The model is a useful tool to determine the treatment strategies during flood session for a large group of patients.