Narrow Results

This paper portrays the exploitation/exploration of artificial intelligence (AI) inspired computing to study the behavior of the multi-delay differential systems that revealed the impact of latent period and the dynamics of the a susceptible, vaccinated, exposed, infectious and recovered (SVEIR) epidemic model involving vaccination by means of the neural networks backpropagation with Levenberg–Marquardt scheme (NNs-BLMS). The reference solutions of the five classes ordinary differential equations (ODEs) model of SVEIR dynamics are calculated by applying the Adams method for variation in delay due to the time spent in preventing the infection and delay due to the duration of recovery immunity in the cured population. The designed NNs-BLMS used the created dataset arbitrarily for training, validation, as well as, testing samples to determine the estimated results of the nonlinear SVEIR epidemic model involving vaccination impact. The achieved accuracy of the designed NNs-BLMS is authenticated/proven by analyzing the fitness function based on mean square error (MSE), regression analysis, and error histogram for sundry scenarios of SVEIR epidemic system with the impact of vaccination.

The current challenge faced by the global research community is how to effectively address, manage, and control the spread of infectious diseases. This research focuses on conducting a dynamic system analysis of a stochastic epidemic model capable of predicting the persistence or extinction of the dengue disease. Numerical methodology on deterministic procedures, i.e. Adams method and stochastic/probabilistic schemes, i.e. stochastic Runge–Kutta method, is employed to simulate and forecast the spread of disease. This study specifically employs two nonlinear mathematical systems, namely the deterministic vector-borne dengue epidemic (DVBDE) and the stochastic vector-borne dengue epidemic (SVBDE) models, for numerical treatment. The objective is to simulate the dynamics of these models and ascertain their dynamic behavior. The VBDE model segmented the population into the following five classes: susceptible population, infected population, recovered population, susceptible mosquitoes, and the infected mosquitoes. The approximate solution for the dynamic evolution for each population is calculated by generating a significant number of scenarios varying the infected population’s recovery rate, human population birth rate, mosquitoes birth rate, contaminated people coming into contact with healthy people, the mortality rate of people, mosquitos population death rate and infected mosquito contact rate with population that is not infected. Comparative evaluations of the deterministic and stochastic models are presented, highlighting their unique characteristics and performance, through the execution of numerical simulations and analysis of the results.

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

The differential equations having delays take paramount interest in the research community due to their fundamental role to interpret and analyze the mathematical models arising in biological studies. This study deals with the exploitation of knack of artificial intelligence-based computing paradigm for numerical treatment of the functional delay differential systems that portray the dynamics of the nonlinear influenza-A epidemic model (IA-EM) by implementation of neural network backpropagation with Levenberg–Marquardt scheme (NNBLMS). The nonlinear IA-EM represented four classes of the population dynamics including susceptible, exposed, infectious and recovered individuals. The referenced datasets for NNBLMS are assembled by employing the Adams method for sufficient large number of scenarios of nonlinear IA-EM through the variation in the infection, turnover, disease associated death and recovery rates. The arbitrary selection of training, testing as well as validation samples of dataset are utilizing by designed NNBLMS to calculate the approximate numerical solutions of the nonlinear IA-EM develop a good agreement with the reference results. The proficiency, reliability and accuracy of the designed NNBLMS are further substantiated via exhaustive simulations-based outcomes in terms of mean square error, regression index and error histogram studies.