Exploring Radial Kernel on the Novel Forced SEYNHRV-S Model to Capture the Second Wave of COVID-19 Spread and the Variable Transmission Rate

The transmission rate of COVID-19 varies over time. There are many reasons underlying this mechanism, such as seasonal changes, lockdowns, social distancing, and wearing face masks. Hence, it is very difficult to directly measure the transmission rate. The main task of the present paper was to identify the variable transmission rate (β1) for a SIR-like model. For this, we first propose a new compartmental forced SEYNHRV-S differential model. We then drive the nonlinear differential equation and present the finite difference technique to obtain the time-dependent transmission rate directly from COVID-19 data. Following this, we show that the transmission rate can be represented as a linear combination of radial kernels, where several forms of radial kernels are explored. The proposed model is flexible and general, so it can be adapted to monitor various epidemic scenarios in various countries. Hence, the model may be of interest for policymakers as a tool to evaluate different possible future scenarios. Numerical simulations are presented to validate the prediction of our SEYNHRV and forced SEYNHRV-S models, where the data from confirmed COVID-19 cases reported by the Ministry of Health in Saudi Arabia were used. These confirmed cases show the second wave of the infected population in Saudi Arabia. By using the COVID-19 data, we show that our model (forced SEYNHRV-S) is able to predict the second wave of infection in the population in Saudi Arabia. It is well known that COVID-19 epidemic data cannot be accurately represented by any compartmental approach with constant parameters, and this is also true for our SEYNHRV model.