Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference

When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that Rs0>1, and it was noticed that, for Rs<1, the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular.

A stochastic SIQR epidemic model with Lévy jumps and three-time delays.

Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China.

A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus.

A new co-infection model for the transmission dynamics of two virus hepatitis B (HBV) and coronavirus (COVID-19) is formulated to study the effect of white noise intensities. First, we present the model equilibria and basic reproduction number. The local stability of the equilibria points is proved. Moreover, the proposed stochastic model has been investigated for a non-negative solution and positively invariant region. With the help of Lyapunov function, analysis was performed and conditions for extinction and persistence of the disease based on the stochastic co-infection model were derived. Particularly, we discuss the dynamics of the stochastic model around the disease-free state. Similarly, we obtain the conditions that fluctuate at the disease endemic state holds if min ( R H s , R C s , R HC s ) > 1 . Based on extinction as well as persistence some conditions are established in form of expression containing white noise intensities as well as model parameters. The numerical results have also been used to illustrate our analytical results.

A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R0≤1. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R0≈1.1367. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically.

Theoretical and numerical analysis of COVID-19 pandemic model with non-local and non-singular kernels.

The global consequences of Coronavirus (COVID-19) have been evident by several hundreds of demises of human beings; hence such plagues are significantly imperative to predict. For this purpose, the mathematical formulation has been proved to be one of the best tools for the assessment of present circumstances and future predictions. In this article, we propose a fractional epidemic model of coronavirus (COVID-19) with vaccination effects. An arbitrary order model of COVID-19 is analyzed through three different fractional operators namely, Caputo, Atangana-Baleanu-Caputo (ABC), and Caputo-Fabrizio (CF), respectively. The fractional dynamics are composed of the interaction among the human population and the external environmental factors of infected peoples. It gives an extra description of the situation of the epidemic. Both the classical and modern approaches have been tested for the proposed model. The qualitative analysis has been checked through the Banach fixed point theory in the sense of a fractional operator. The stability concept of Hyers-Ulam idea is derived. The Newton interpolation scheme is applied for numerical solutions and by assigning values to different parameters. The numerical works in this research verified the analytical results. Finally, some important conclusions are drawn that might provide further basis for in-depth studies of such epidemics.

STOCHASTIC OPTIMAL CONTROL ANALYSIS FOR THE COVID-19 EPIDEMIC MODEL UNDER REAL STATISTICS

The COVID-19 pandemic started, a global effort to develop vaccines and make them available to the public, has prompted a turning point in the history of vaccine development. In this study, we formulate a stochastic COVID-19 epidemic mathematical model with a vaccination effect. First, we present the model equilibria and basic reproduction number. To indicate that our stochastic model is well-posed, we prove the existence and uniqueness of a positive solution at the beginning. The sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established. For controlling the transmission of the disease by the application of external sources, the theory of stochastic optimality is established. The nonlinear least-squares procedure is utilized to parametrize the model from actual cases reported in Pakistan. The numerical simulations are carried out to demonstrate the analytical results. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

Several mathematical models have been developed to investigate the dynamics SARS-CoV-2 and its different variants. Most of the multi-strain SARS-CoV-2 models do not capture an important and more realistic feature of such models known as randomness. As the dynamical behavior of most epidemics, especially SARS-CoV-2, is unarguably influenced by several random factors, it is appropriate to consider a stochastic vaccination co-infection model for two strains of SARS-CoV-2. In this work, a new stochastic model for two variants of SARS-CoV-2 is presented. The conditions of existence and the uniqueness of a unique global solution of the stochastic model are derived. Constructing an appropriate Lyapunov function, the conditions for the stochastic system to fluctuate around endemic equilibrium of the deterministic system are derived. Stationary distribution and ergodicity for the new co-infection model are also studied. Numerical simulations are carried out to validate theoretical results. It is observed that when the white noise intensities are larger than certain thresholds and the associated stochastic reproduction numbers are less than unity, both strains die out and go into extinction with unit probability. More-over, it was observed that, for weak white noise intensities, the solution of the stochastic system fluctuates around the endemic equilibrium (EE) of the deterministic model. Frequency distributions are also studied to show random fluctuations due to stochastic white noise intensities. The results presented herein also reveal the impact of vaccination in reducing the co-circulation of SARS-CoV-2 variants within the given population.

Impact of information and Lévy noise on stochastic COVID-19 epidemic model under real statistical data.

In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.

Fractal fractional based transmission dynamics of COVID-19 epidemic model.

We investigate the dynamical behavior of Coronavirus (COVID-19) for different infections phases and multiple routes of transmission. In this regard, we study a COVID-19 model in the context of fractal-fractional order operator. First, we study the COVID-19 dynamics with a fractal fractional-order operator in the framework of Atangana-Baleanu fractal-fractional operator. We estimated the basic reduction number and the stability results of the proposed model. We show the data fitting to the proposed model. The system has been investigated for qualitative analysis. Novel numerical methods are introduced for the derivation of an iterative scheme of the fractal-fractional Atangana-Baleanu order. Finally, numerical simulations are performed for various orders of fractal-fractional dimension.

On the Analysis of Caputo Fractional Order Dynamics of Middle East Lungs Coronavirus (MERS-CoV) Model

The current paper deals with the transmission of MERS-CoV model between the humans populace and the camels, which are suspected to be the primary source for the infection. The effect of time MERS-CoV disease transmission is explored using a non-linear fractional order in the sense of Caputo operator in this paper. The considered model is analyzed for the qualitative theory, uniqueness of the solution are discussed by using the Banach contraction principle. Stability analysis is investigated by the aid of Ulam-Hyres (UH) and its generalized version. Finally, we show the numerical results with the help of generalized Adams-Bashforth-Moulton Method (GABMM) are used for the proposed model, for supporting our analytical work.

Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel type operator known as the Atangana-Baleanu-Caputo (ABC) derivative. We parametrize the model adopting available information of the disease from Pakistan in the period 9 April to 2 June 2020. We obtain the required solution with the help of a hybrid method, which is a combination of the decomposition method and the Laplace transform. Furthermore, a sensitivity analysis is carried out to evaluate the parameters that are more sensitive to the basic reproduction number of the model. Our results are compared with the real data of Pakistan and numerical plots are presented at various fractional orders.

Stochastic COVID-19 SEIQ epidemic model with time-delay.

In this work, we consider an epidemic model for corona-virus (COVID-19) with random perturbations as well as time delay, composed of four different classes of susceptible population, the exposed population, the infectious population and the quarantine population. We investigate the proposed problem for the derivation of at least one and unique solution in the positive feasible region of non-local solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function in the sense of delay-stochastic approach and the condition for the extinction of the disease is also established. Our obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been numerically simulated.

A vigorous study of fractional order COVID-19 model via ABC derivatives.

The newly arose irresistible sickness known as the Covid illness (COVID-19), is a highly infectious viral disease. This disease caused millions of tainted cases internationally and still represent a disturbing circumstance for the human lives. As of late, numerous mathematical compartmental models have been considered to even more likely comprehend the Covid illness. The greater part of these models depends on integer-order derivatives which cannot catch the fading memory and crossover behavior found in many biological phenomena. Along these lines, the Covid illness in this paper is studied by investigating the elements of COVID-19 contamination utilizing the non-integer Atangana-Baleanu-Caputo derivative. Using the fixed-point approach, the existence and uniqueness of the integral of the fractional model for COVID is further deliberated. Along with Ulam-Hyers stability analysis, for the given model, all basic properties are studied. Furthermore, numerical simulations are performed using Newton polynomial and Adams Bashforth approaches for determining the impact of parameters change on the dynamical behavior of the systems.

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China.

Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin's maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme.

On a new conceptual mathematical model dealing the current novel coronavirus-19 infectious disease.

The present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.

Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model.

Similar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019. The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere. Assuming that the spread of virus follows a random process instead of deterministic. The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables. The proposed study is devoted to investigate a model consist of three exclusive compartments. The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals. We discuss the model's extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease' extinction. Lastly, the numerical simulation is executed for supporting the theoretical findings.