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An epidemic disease caused by coronavirus has spread all over the world with a strong contagion rate. We present simulations of epidemic models constructed using real data to give a clear perspective and confirmation on the effect of quarantine on the evolution of the infection and the number of infected, recovered, and dead because of this epidemic in South Carolina in a time window (December 1, 2020, to June 1, 2021) when the epidemic was relatively strong. We use CDC data for infected and dead populations covering the period December 1, 2020, to June 1, 2021 in South Carolina to develop models and do simulations. There were no data available for recovered populations in this period. Part of our goal is to estimate the number of recovered for the entire period. The models and results are consistent with the data. The infection and recovery increasing in South Carolina do not show improvement in this period. The number of dead people in this period tended to increase although by small amount. Optimal control methodologies are considered where transmission, recovery, relapse of immunity and death rates are considered as decision variables in minimizing the difference between the real and computed COVID-19 infection and dead data. Effect of quarantine as intervention strategy is also considered as it is critical issue. What we want to show is what could have been the outcome if quarantine had been implemented from the very beginning. The progress of an infection in general is related not only to the present states, but also to its historical states. To account for the effect of past evolution we add fractional differential equations models. 

Connected vehicle (CV) systems are cognizant of potential cyber attacks because of increasing connectivity between its different components such as vehicles, roadside infrastructure and traffic management centers. However, it is a challenge to detect security threats in real-time and develop appropriate/effective countermeasures for a CV system because of the dynamic behavior of such attacks, high computational power requirement and a historical data requirement for training detection models. To address these challenges, statistical models, especially change point models, have potentials for real-time anomaly detections. Thus, the objective of this study is to investigate the efficacy of two change point models, Expectation Maximization (EM) and two forms of Cumulative Summation (CUSUM) algorithms (i.e., typical and adaptive), for real-time V2I cyber attack detection in a CV Environment. To prove the efficacy of these models, we evaluated these two models for three different type of cyber attack, denial of service (DOS), impersonation, and false information, using basic safety messages (BSMs) generated from CVs through simulation. Results from numerical analysis revealed that EM, CUSUM, and adaptive CUSUM could detect these cyber attacks, DOS, impersonation, and false information, with an accuracy of (99\%, 100\%, 100\%), (98\%, 100\%, 100\%), and (100\%, 98\%, 100\%) respectively.