A mathematical model and simulation scenarios for T and B cells immune response to severe acute respiratory syndrome-coronavirus-2

Severe acute respiratory syndrome coronavirus is a type 2 highly contagious, and transmissible among humans;the natural human immune response to severe acute respiratory syndrome-coronavirus-2 combines cell-mediated immunity (lymphocyte) and antibody production. In the present study, we analyzed the dynamic effects of adaptive immune system cell activation in the human host. The methodology consisted of modeling using a system of ordinary differential equations;for this model, the equilibrium free of viral infection was obtained, and its local stability was determined. Analysis of the model revealed that lymphocyte activation leads to total pathogen elimination by specific recognition of viral antigens;the model dynamics are driven by the interaction between respiratory epithelial cells, viral infection, and activation of helper T, cytotoxic T, and B lymphocytes. Numerical simulations showed that the model solutions match the dynamics involved in the role of lymphocytes in preventing new infections and stopping the viral spread;these results reinforce the understanding of the cellular immune mechanisms and processes of the organism against severe acute respiratory syndrome-coronavirus-2 infection, allowing the understanding of biophysical processes that occur in living systems, dealing with the exchange of information at the cellular level.

THREE-DIMENSIONAL ANALYTICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION FOR AIR POLLUTION DISPERSION

We develop a new analytical solution of a three-dimensional atmospheric pollutant dispersion. The main idea is to subdivide vertically the planetary boundary layer into sub-layers, where the wind speed and eddy diffusivity assume average values for each sub-layer. Basically, the model is assessed and validated using data obtained from the Copenhagen diffusion and Prairie Grass experiments. Our findings show that there is a good agreement between the predicted and observed crosswind-integrated concentrations. Moreover, the calculated statistical indices are within the range of acceptable model performance.

Analytical and Numerical Investigation of the SIR Mathematical Model

This is a theoretical study of the SIR model — a popular mathematical model of the propagation of infectious diseases. We construct a solution of the Cauchy problem for a system of two ordinary differential equations describing in integral form the concentration dynamics of infected and recovered individuals in an immune population. A qualitative analysis is carried out of the stationary system states using the Lyapunov function. An expression is obtained for the coordinates of the equilibrium points in terms of the Lambert W-function for arbitrary initial values. The application of the SIR model for the description of COVID-19 propagation dynamic is demonstrated. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach's accuracy and utility, and it is presented in symmetric forms.

Data Driven Modeling Social Media Influence using Differential Equations

Individuals modify their opinions towards a topic based on their social interactions. Opinion evolution models conceptualize the change of opinion as a uni-dimensional continuum, and the effect of influence is built by the group size, the network structures, or the relations among opinions within the group. However, how to model the personal opinion evolution process under the effect of the online social influence as a function remains unclear. Here, we show that the uni-dimensional continuous user opinions can be represented by compressed high-dimensional word embeddings, and its evolution can be accurately modelled by an ordinary differential equation (ODE) that reflects the social network influencer interactions. We perform our analysis on 87 active users with corresponding influencers on the COVID-19 topic from 2020 to 2022. The regression results demonstrate that 99% of the variation in the quantified opinions can be explained by the way we model the connected opinions from their influencers. Our research on the COVID-19 topic and for the account analysed shows that social media users primarily shift their opinion based on influencers they follow (e.g., model explains for 99% variation) and self-evolution of opinion over a long time scale is limited. © 2022 IEEE.

Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach

We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. The objective of this research was to halt the global spread of a disease. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.

Analyzing the effect of restrictions on the COVID-19 outbreak for some US states.

The ongoing pandemic disease COVID­19 has caused worldwide social and financial disruption. As many countries are engaged in designing vaccines, the harmful second and third waves of COVID­19 have already appeared in many countries. To investigate changes in transmission rates and the effect of social distancing in the USA, we formulate a system of ordinary differential equations using data of confirmed cases and deaths in these states: California, Texas, Florida, Georgia, Illinois, Louisiana, Michigan, and Missouri. Our models and their parameter estimations show social distancing can reduce the transmission of COVID­19 by 60% to 90%. Thus, obeying the movement restriction rules is crucial in reducing the magnitude of the outbreak waves. This study also estimates the percentage of people who were not social distancing ranges between 10% and 18% in these states. Our analysis shows the management restrictions taken by these states do not slow the disease progression enough to contain the outbreak.

A parallel approach to the fractional time delay model for predicting the spread of COVID-19

Due to the importance of forecast accuracy for diseases such as COVID-19, the existence of a mathematical model is particularly important. In this research, first, a model to describe the spread of the COVID-19 pandemic is examined. This model is based on a fractional ordinary differential equation. Then the predictor-corrector numerical method is presented to solve this model. Due to the computational challenge of numerically solving fractional models, a task-parallel approach with coarse granularity is presented to solve this model on shared memory systems. The initial data for testing the proposed approach is the data reported on December 31, 2019 by the Wuhan Municipal Commission of the outbreak of the COVID-19 pandemic in the city of Wuhan, China. The numerical results obtained from the proposed parallel approach show that the speedup of the parallel method compared to the sequential method reaches 2.76 in the prediction of 1000 days. © 2022 IEEE.

Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that have a similar fashion of transmission via sharp objects contaminated by viruses, transplant surgery, transfusion, and sexual relations. Simultaneous infections with HTLV-I and HIV-1 usually occur in areas where both viruses have become endemic. CD4+T cells are the main targets of HTLV-I, while HIV-1 can infect CD4+T cells and macrophages. It is the aim of this study to develop a model of HTLV-I and HIV-1 coinfection that describes the interactions of nine compartments: susceptible cells of both CD4+T cells and macrophages, HIV-1-infected cells that are latent/active in both CD4+T cells and macrophages, HTLV-I-infected CD4+T cells that are latent/active, and free HIV-1 particles. The well-posedness, existence of equilibria, and global stability analysis of our model are investigated. The Lyapunov function and LaSalle's invariance principle were used to study the global asymptotic stability of all equilibria. The theoretically predicted outcomes were verified by utilizing numerical simulations. The effect of including the macrophages and latent reservoirs in the HTLV-I and HIV-1 coinfection model is discussed. We show that the presence of macrophages makes a coinfection model more realistic when the case of the coexistence of HIV-1 and HTLV-I is established. Moreover, we have shown that neglecting the latent reservoirs in HTLV-I and HIV-1 coinfection modeling will lead to the design of an overflow of anti-HIV-1 drugs.

COVID-19 Suppression Using a Testing/Quarantine Strategy: A Multi-Paradigm Simulation Approach Based on a SEIRTQ Compartmental Model

During the current COVID-19 pandemic, non-pharmaceutical interventions represent the first-line of defense to tackle the dispersion of the disease. One of the main non-pharmaceutical interventions is testing, which consists on the application of clinical tests aiming to detect and quarantine infected people. Here, we extended the SEIR compartmental model into a SEIRTQ model, adding new states representing the testing (T) and quarantine (Q) dynamics. In doing so, we have characterized the effects of a set of testing and quarantine strategies using a multi-paradigm approach, based on ordinary differential equations and agent based modelling. Our simulations suggest that iterative testing over 10% of the population could effectively suppress the spread of COVID-19 when testing results are delivered within 1 day. Under these conditions, a reduction of at least 95% of the infected individuals can be achieved, along with a drastic reduction in the number of super-spreaders. © 2022 IEEE.

Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models.

Checking the models about the ongoing Coronavirus Disease 2019 (COVID-19) pandemic is an important issue. Some famous ordinary differential equation (ODE) models, such as the SIR and SEIR models have been used to describe and predict the epidemic trend. Still, in many cases, only part of the equations can be observed. A test is suggested to check possibly partially observed ODE models with a fixed design sampling scheme. The asymptotic properties of the test under the null, global and local alternative hypotheses are presented. Two new propositions about U-statistics with varying kernels based on independent but non-identical data are derived as essential tools. Some simulation studies are conducted to examine the performances of the test. Based on the available public data, it is found that the SEIR model, for modeling the data of COVID-19 infective cases in certain periods in Japan and Algeria, respectively, maybe not be appropriate by applying the proposed test.

Stability analysis of a model of epidemic dynamics with nonlinear feedback producing recurrent infection waves

Complex dynamics characterizing human behavior in an epidemiological scenario can be modeled via a system of ordinary differential equations starting from a simple SIR (susceptible–infected–recovered) model. Here we propose a nonlinear mathematical model that describes the evolution in time of susceptible, infected and hospitalized individuals. A new variable that reflects the society's "memory" of the severity of the epidemic is introduced, and this variable feeds back on the transmission rate of the disease. The nonlinear transmission rate reflects the fact that changes (e.g., an increase) in the number of hospitalized individuals can influence the behavior of society and individuals, which would affect (reduce) the probability of transmission. Differently from the standard SIR model, the nonlinear transmission rate may lead to complex dynamics with oscillatory solutions due to a Hopf bifurcation. Such oscillations correspond to recurrent infection waves. Using two parameter bifurcation diagrams we investigate the parameter space of the model. Finally, we report two examples on how the multiple infection waves present for the COVID-19 pandemic can be fitted by our model. [ FROM AUTHOR]

A novel framework based on network embedding for the simulation and analysis of disease progression

Modelling infectious disease spreading is crucial for planning effective containment measures, as shown in the COVID-19 pandemic. The effectiveness of planned measures can also be measured regarding saved lives and economic resources. Therefore, introducing methods able to model the evolution and the impact of measures, as well as planning tailored and updated measures, is a crucial step. Existing models for spreading modelling belong to two main classes: (i) compartmental models based on ordinary differential equations and (ii) contact-based models based on a contact structure using an underlining layer to simulate diffusion. Nevertheless, none of these methods can leverage the high computational power of artificial intelligence and deep learning. We propose a novel framework for simulating and analysing disease progression for these methods. The framework is based on the multiscale simulation of the spreading based on using a multiscale contact model built on top of a diffusion model customised by the user. The evolution of the spreading, modelled as a graph with attributed nodes, is then mapped into a latent space through graph embedding. Finally, deep learning models are used in the latent space to analyse and forecast methods without running expensive computational simulations of the contact-based model. © 2022 IEEE.

Optimization of Coronavirus Pandemic Model Through Artificial Intelligence

Artificial intelligence is demonstrated by machines, unlike the natural intelligence displayed by animals, including humans. Artificial intelligence research has been defined as the field of study of intelligent agents,which refers to any system that perceives its environment and takes actions that maximize its chance of achieving its goals. The techniques of intelligent computing solve many applications of mathematical modeling. The researchworkwas designed via a particularmethod of artificial neural networks to solve the mathematical model of coronavirus. The representation of the mathematical model is made via systems of nonlinear ordinary differential equations. These differential equations are established by collecting the susceptible, the exposed, the symptomatic, super spreaders, infection with asymptomatic, hospitalized, recovery, and fatality classes. The generation of the coronavirus model's dataset is exploited by the strength of the explicit Runge Kutta method for different countries like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, validation, and testing processes for each cyclic update in Bayesian Regularization Backpropagation for the numerical treatment of the dynamics of the desired model. The performance and effectiveness of the designed methodology are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis. © 2023 Tech Science Press. All rights reserved.

Applying a suitable approximate-simulation technique of an epidemic model with random parameters

In this research, a suitable numerical simulation method is used to solve a non-linear system that contains multi -variables and multi-parameters with absent real data. The solution to such type of system needs a long time with some difficulty. Mean Latin Hypercube Runge Kutta (MLH RK4) propused method solve such system that has random parameters easily and fast. In addition, it is the appropriate method for solving the change in the values of the system coefficients with time. The mentioned system has been given realistic results with MLH RK4 that has been applied to the epidemic model. The COVID-19 model from 2020 in Iraq is the application under the research. The comparison study between the numerical results with the proposed numerical simulation results is shown in tables, and more clear graphically. The COVID-19 pandemic in our study will vanish in the next few years, according to the behavior of the epidemic for all its stages mentioned in our study. The proposed method can lessen the number of iterations for the used numerical method, and the number of repetitions of the used simulation technique. As well as it is a faster technique in the generation of parameters that appears as random variables using the Latin Hypercube sampling technique. The MLH RK4 method has been confirmed to be reliable, and effective to solve linear and nonlinear problems. The proposed method can predict the behavior of phases of the epidemic in the future of some epidemiological models.

The Kermack-McKendrick model in the spread of COVID-19 strains: Peru 2020-2021

Introduction: The SIR epidemic model is useful for measuring the rate of spread of COVID-19 strains (B.1.617.2/P.1/C.37/B.1.621), in terms of epidemiological threshold R0 over time. Objective: To evaluate a mathematical model of differential type, typical of the behavior of COVID-19 for the Peruvian collective. Methods: A differential mathematical model of the behavior of the pandemic was developed for the Peruvian collective, based on the experience in the control of Kermack-McKendrick infections. The number of susceptible S, infected and spreading infection I and recovered R was estimated, using official datasets from the World Health Organization, based on the history between March 7 and September 12, 2020 and;projected for 52 weeks until September 11,2021. Results: The lowest rate of infections will occur from April 3, 2021. Evidencing a prognosis of lower transmissibility for May 29, 2021 with an infected rate (ß=0.08) and threshold (R0=0.000), the accuracy of the model was also quantified at 97.795%, with 2.205% of average percentage error, with the temporary average value being R0 <1, so each person who contracts the disease will infect less than one person before dying or recovering, so the outbreak will disappear. Conclusion: The curve of infections in Peru will depend directly on mitigation measures to curb the spread of infection and predict sustained transmission through vaccination against covid-19 type strains;with the observance of people of preventive measures.Alternate :Introducción: El modelo epidémico SIR es útil para medir la velocidad de propagación de las cepas COVID-19 (B.1.617.2/P.1/C.37/B.1.621), en términos de umbral epidemiológico R[sub]0[/sub] a lo largo del tiempo. Objetivo: Evaluar un modelo matemático de tipo diferencial, propio del comportamiento del COVID-19 para el colectivo peruano. Métodos: Se desarrolló un modelo matemático diferencial del comportamiento de la pandemia para el colectivo peruano, partiendo de la experiencia en el control de infecciones Kermack-McKendrick. Se estimó el número de susceptibles S, infectados y diseminando la infección I y recuperados R, con el uso de conjuntos de datos oficiales de la Organización Mundial de la Salud, partiendo del histórico entre el 07 de marzo y el 12 de septiembre de 2020 y;proyectado durante 52 semanas hasta el 11 de septiembre de 2021. Resultados: La menor tasa de infectados ocurrirá a partir del 3 de abril de 2021. Evidenciando un pronóstico de menor transmisibilidad para el 29 de mayo de 2021 con una tasa de infectados (ß=0.08) y umbral (R0=0,000), además se cuantificó la exactitud del modelo en 97,795 %, con 2,205 % de error porcentual medio, siendo el valor promedio temporal R0 <1, así que cada persona que contrae la enfermedad infectará a menos de una persona antes de morir o recuperarse, por lo que el brote desaparecerá. Conclusión: La curva de contagios en el Perú dependerá directamente de las medidas de mitigación para frenar la propagación de la infección y predecir una transmisión sostenida a través de la vacunación contra las cepas tipo del COVID-19;con la observancia de las personas de las medidas preventivas.

Differential Evolution to Optimize A Long-term Multi-strain Model of COVID-19 in South Africa

A limited number of studies have been conducted to investigate the dynamics of COVID-19 disease spread in South Africa and these existing studies have mostly focussed on mathematical analysis of a relatively short time period near the initial outbreak of COVID-19 in South Africa. The current study therefore attempted to extend on previous studies by applying a Susceptible- Exposed - Infected - Removed (SEIR) disease model to analyse the long-term dynamics of COVID-19 in South Africa, taking into account multiple waves of infection potentially caused by different virus strains. A Differential Evolution (DE) algorithm was used to fit the proposed model to real-world data, and this was done on both a geographically local and global scale to investigate the differences between these two approaches. Results revealed that a local approach provided a more accurate model fit to data than a global approach and that the method proposed in this work could give valuable insights into disease dynamics. © 2022 IEEE.

Age-related model for estimating the symptomatic and asymptomatic transmissibility of COVID-19 patients.

Estimation of age-dependent transmissibility of COVID-19 patients is critical for effective policymaking. Although the transmissibility of symptomatic cases has been extensively studied, asymptomatic infection is understudied due to limited data. Using a dataset with reliably distinguished symptomatic and asymptomatic statuses of COVID-19 cases, we propose an ordinary differential equation model that considers age-dependent transmissibility in transmission dynamics. Under a Bayesian framework, multi-source information is synthesized in our model for identifying transmissibility. A shrinkage prior among age groups is also adopted to improve the estimation behavior of transmissibility from age-structured data. The added values of accounting for age-dependent transmissibility are further evaluated through simulation studies. In real-data analysis, we compare our approach with two basic models using the deviance information criterion (DIC) and its extension. We find that the proposed model is more flexible for our epidemic data. Our results also suggest that the transmissibility of asymptomatic infections is significantly lower (on average, 76.45% with a credible interval (27.38%, 88.65%)) than that of symptomatic cases. In both symptomatic and asymptomatic patients, the transmissibility mainly increases with age. Patients older than 30 years are more likely to develop symptoms with higher transmissibility. We also find that the transmission burden of asymptomatic cases is lower than that of symptomatic patients.

A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus

In this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical systems theory will be performed by studying the local behavior of the equilibrium points and obtaining the local dynamics properties from the linear stability point of view. Additionally, we will compare these models in order to understand which is more appropriate to model the interaction between the human immune system and a virus. Some natural medical interpretations will be obtained, which are available for all three models and can be useful to the medical community.