Novel neuro-stochastic adaptive supervised learning for numerical treatment of nonlinear epidemic delay differential system with impact of double diseases
Nabeela Anwar, Iftikhar Ahmad, Adiqa Kausar Kiani, Muhammad Shoaib, Muhammad Asif Zahoor Raja
Abstract
This paper presents a novel neuro-stochastic adaptive processing to investigate the dynamic behavior of the nonlinear SIS epidemic delayed model with the impact of double disease (SIS-EDDM) using the knack of prediction and modeling of artificial neural networks (ANNs) optimized through Levenberg-Marquardt technique (LMT), i.e. ANNs-LMT. The model captures the dynamic progression of individuals in the population, differentiating between those susceptible to infection and affected by two unique viruses. The inclusion of time delays in the differential equations introduces a critical temporal aspect to the model, enhancing its precision in portraying the transmutation process. The reference dataset for ANNs-LMT is produced using the explicit Runge-Kutta method, with variations in the transmission coefficients between susceptible and infective populations, the death rate of infective population caused by diseases, the cure rate of treatment for infected population, vaccination proportional coefficient for the susceptible population, white noise of the environment, and time delay. The designed computing framework of ANNs-LMT is used to determine the numerical solutions of the variants of SIS-EDDM by incorporating the training, testing, and validation samples based adaptive learning processing. The neuro-stochastic adaptive processing of ANNs-LMT is validated by minimal absolute and mean squared errors, coupled with the attainment of nearly optimal regression measures, demonstrating its accuracy and effectiveness.