N. Begashaw, Gurcan Comert, and N. G. Medhin
Modeling Covid-19 Epidemic with Quarantine and Lockdown and Analysis
Dynamic Systems and Applications 32 (2023) No.4, 275-293

https://doi.org/10.46719/dsa2023.32.15

ABSTRACT:
An epidemic disease caused by coronavirus has spread all over the world with a strong contagion rate. We implement an SIR model to study the evolution of the infected population and the number of infected recovered and dead because of this epidemic in South Carolina consistent with available data. We perform an analysis of the results of the model by varying the parameters and initial conditions, in particular transmission and recovery rates.

We use data covering the period December 1, 2020, to June 1, 2021. The models and results are consistent with the observations. The models developed using data help us understand the recovery rates. The infection and recovery increasing in South Carolina do not show improvement. The number of dead people tends to increase although by small amount.    

Models were developed based on the available data. Initially neural networks and machine learning methodology were used to come up with transmission rates. Later, direct calculation and optimal control methodology were used to deduce transmission parameters. For the period December to June there were no available data on recovered populations, and we have to determine them as well as transmission and recovery rates based on data of infected populations and dead population using neural networks and optimal control methodologies where transmission, recovery, relapsation immunity and death rates from infection are considered as decision variables.

From the data from CDC, we see that the number of infected population is increasing. We have also data for the number of dead population due to the virus. Our models are consistent with the data we have available for the infected and dead population. However, there were no data for recovered population in South Carolina for the entire period December 1 to June 1. We have to use our model to come up with a recovered population number. One thing we observe is that the number of infected populations was increasing. One of the control measures that are believed to be reliable methods of curbing the spread of the virus is quarantine. We include a model that includes quarantine in our work. In our quarantine we see that if 100,000 susceptible people in the whole state were quarantined there would have been a considerable decrease in the number of infected populations.

AMS (MOS) Subject Classification. 34H05, 34D20, 68T07, 92B20
Key Words and Phrases. Optimal control, Reproduction number.