Intelligent solution predictive control strategy for nonlinear hepatitis B epidemic model with delay
Nabeela Anwar, Iftikhar Ahmad, Adiqa Kausar Kiani, Shafaq Naz, Muhammad Shoaib, Muhammad Asif Zahoor Raja
Abstract
This study exploits the artificial neural networks (ANNs) with backpropagation of the Levenberg-Marquardt method (LMM), i.e. ANNs-LMM, to explore the dynamics of a nonlinear hepatitis B epidemic model with the effect of delay (HBEMD). A system of three nonlinear ordinary differential equations having delay describes the susceptible liver cells, infected liver cells, and density of CTLs in the epidemic model. The referenced dataset is generated using the strength of the implicit Runge–Kutta numerical method in the variation of the incidence rate of disease, CTL immunological response rate of removing the disease-infected cells, virus specific CTL cells reproduction rate due to interaction with virally infected cells, time delay, white noise densities, and morality rate of individuals, infected cells death rate and virus specific CTL cells removing rate. The generated dataset is arbitrarily utilized for training, testing, and validation operations for each recurrent update in the Levenberg-Marquardt backpropagation to determine the numerical solutions for the dynamics of HBEMD. The effectiveness and reliability of the intelligent solution predictive control strategy of ANNs-LMM are endorsed with negligible absolute errors, mean square errors and near optimal regression measures.