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In this study, an intelligent computing framework is presented to explore the influence of unpredictable environmental factors on the spread of infections. A stochastic non-linear SIS epidemic model (SISEM) is examined that incorporates a non-linear incidence rate, and impact of random fluctuations on the disease transmission. The knacks of artificial neural networks Levenberg–Marquardt (ANNLMA) technique are exploited to illustrate the behavioral complexities of stochastic non-linear SISEM, which explores the dynamics of disease transmission in a stochastic environment and provides insights into the interactions between susceptible and infectious populations. The Milstein approach of order 1 generates a dataset for the proposed ANNLMA technique by varying integrated parameters, such as the rates of recovery, death, disease transmission, noise standard deviation and the entire population, for various SISEM scenarios. The referenced dataset is randomly divided into test, validation and train sets for the weight learning of the proposed ANNLMA. The viability of the ANNLMA is measured using intensive simulation-based investigations through analysis of mean squared errors, histograms, regression and autocorrelation studies. The investigations highlighted that the ANNLMA results closely match the reference results, illustrating convergence within the 10−2 to 10−7 range, indicating the validity of the proposed methodology. [ABSTRACT FROM AUTHOR]

Oncolytic viral immunotherapy is gaining considerable prominence in the realm of chronic diseases treatment and rehabilitation. Oncolytic viral therapy is an intriguing therapeutic approach due to its low toxicity and dual function of immune stimulations. This work aims to design a soft computing approach using stupendous knacks of neural networks (NNs) optimized with Bayesian regularization (BR), i.e. NNs-BR, procedure. The constructed NNs-BR technique is exploited in order to determine the approximate numerical treatment of the nonlinear multi-delayed tumor virotherapy (TVT) models in terms of the dynamic interactions between the tumor cells free of viruses, tumor cells infected by viruses, viruses, and cytotoxic T-lymphocytes (CTLs). The strength of state-of-the-art numerical approach is incorporated to develop the reference dataset for the variation in the infection rate for tumor cells, virus-free tumor cell clearance rate by CTLs, CTLs clearance rate for infectious tumor cells, the natural lifecycle of infectious tumor cells, the natural lifecycle of viral cell, the natural lifecycle of CTLs cells, tumor cells free of viruses' maximum proliferation rate, production of tumor cells with an infection, CTLs simulated ratio for infectious tumor cells, CTLs simulated ratios for virus-free cells and delay in time. The dataset is randomly chosen/segmented for training-testing-validation samples to construct the NNs models optimized with backpropagated BR representing the approximate numerical solutions of the dynamic interactions in the TVT model. The performance of the designed NNs-BR technique is accessed/evaluated and outcomes are found in good agreement with the reference solutions having the range of accuracy from 10 − 9 to 10 − 1 6 . The efficacy of NNs-BR paradigm is further substantiated after rigorous analysis on regression metrics, learning curves on MSE, and error histograms for the dynamics of TVT model. [ABSTRACT FROM AUTHOR]

In this article, we analyze the dynamics of the non-linear tumor-immune delayed (TID) model illustrating the interaction among tumor cells and the immune system (cytotoxic T lymphocytes, T helper cells), where the delays portray the times required for molecule formation, cell growth, segregation, and transportation, among other factors by exploiting the knacks of soft computing paradigm utilizing neural networks with back propagation Levenberg Marquardt approach (NNLMA). The governing differential delayed system of non-linear TID, which comprised the densities of the tumor population, cytotoxic T lymphocytes and T helper cells, is represented by non-linear delay ordinary differential equations with three classes. The baseline data is formulated by exploiting the explicit Runge-Kutta method (RKM) by diverting the transmutation rate of Tc to Th of the Tc population, transmutation rate of Tc to Th of the Th population, eradication of tumor cells through Tc cells, eradication of tumor cells through Th cells, Tc cells' natural mortality rate, Th cells' natural mortality rate as well as time delay. The approximated solution of the non-linear TID model is determined by randomly subdividing the formulated data samples for training, testing, as well as validation sets in the network formulation and learning procedures. The strength, reliability, and efficacy of the designed NNLMA for solving non-linear TID model are endorsed by small/negligible absolute errors, error histogram studies, mean squared errors based convergence and close to optimal modeling index for regression measurements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Alcohol abuse is a substantial cause of various health and societal issues, as well as a significant factor in global disease. Once alcohol is consumed in the gastrointestinal tract, it undergoes metabolism in the liver and lungs. In this investigation, the nonlinear deterministic and stochastic differential frameworks are analyzed numerically to predict the dynamic evolution of the virus in the drinker alcohol model. The framework for apprehending drinking patterns is categorized into three distinct groups: the susceptible population, risk drinkers, and moderate drinkers. The approximate solution for each population group is determined by exhaustively creating scenarios that vary the probability ratio of infection in susceptible individuals who do not consume alcohol, the increasing rate of alcohol consumption, the rate at which individuals transition from acute to chronic drinking categories, the rate at which new non-drinking consumers are attracted, the death rate of the population, the ratio affecting the rate of sociability in heavy drinkers, and the overall population rate. The Euler–Maruyama approach for the stochastic framework and the Adams method for the deterministic framework are utilized, respectively, to determine the solutions of the alcohol drinker model. This study compares deterministic and stochastic frameworks to underscore their distinct characteristics and efficiency, achieved through comprehensive simulations and in-depth analysis of the numerical outcomes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, the artificial intelligence techniques have been used for the solution of Falkner-Skan (FS) equations based on neural networks optimized with three methods including active set technique, sequential quadratic programming and genetic algorithms (GA) hybridization. Log-sigmoid activation function is used in artificial neural network architecture. The proposed techniques are applied to a number of cases for Falkner-Skan problems, and results were compared with GA hybrid results in all cases and were found accurate. The level of accuracy is examined through statistical analyses based on a sufficiently large number of independent runs. [ABSTRACT FROM AUTHOR]