N. Begashaw, Gurcan Comert, N. G. Medhin
Discrete Epidemic Models: Neural Network Approach
Dynamic Systems and Applications 33 (2024)   161-174

https://doi.org/10.46719/dsa2024.33.07

ABSTRACT.
In this paper we consider a discrete epidemic SIR/COVID model. Since models can be used
for early warning and to forecast the behavior of an epidemic and develop intervention strategies it is critical
to be able to effectively predict transmission and recovery rates. Based on available daily infection and death
data from South Carolina for the period December 1, 2020, to June 1, 2021 we develop a discrete model and
analyze evolution of the model using optimization, artificial neural network, machine learning and Grey model
inferring the daily, transmission, and reproduction rates, and recovery for each day of the period.

The models and results are consistent with the observations. The models developed using data help us
understand the recovery and transmission rates, hence the evolution of the epidemic. The infection and
recovery increasing in South Carolina do not show improvement in the period covered. The number of dead
people tends to increase although by small amount. Forecasting data for a short time in the future can be
used to judge the possible evolution of the epidemic and intervention.

Models were developed based on the available data. 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 artificial neural networks and optimization
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 recovered population
number. One thing we observe is that the number of infected population 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
population.

AMS (MOS)Subject Classification. 34H05, 34D20, 68T07, 92B20.

Key Words and Phrases. Optimal control, Reproduction number.