Fractional Order Epidemic System of Saturated Rate of Incidence: A Neural Network Approach

ABSTRACT A fractional order mathematical model of the saturated rate of incidence is solved numerically by applying a neural network scheme. The mathematical fractional order saturated rate of incidence system is classified into four classes of individuals: susceptible, infected, vaccinated, and recovered. The solution of the model is presented in three cases based on the fractional order values of the saturated rate of incidence system to authenticate better performance closer to 0 or 1. The solutions of the model are presented by designing a neural network construction containing Levenberg–Marquardt Backpropagation neural network, a single hidden layer with 10 neurons, and a sigmoid activation function. An Adam numerical scheme is used to get the dataset, which is divided into training, testing, and validation with the ratio of 70%, 20%, and 10%. The capability of the proposed neural network is perceived by the overlapping of the outcomes, small absolute error, and best training values. To validate the solver's reliability, different tests like regression, transition state, and error histogram have also been performed.