In this paper, we explore local dynamics with topological classifications, bifurcation analysis, and chaos control in a discrete-time COVID-19 epidemic model in the interior of . It is explored that for all involved parametric values, discrete-time COVID-19 epidemic model has boundary equilibrium solution and also it has an interior equilibrium solution under definite parametric condition. We have explored the local dynamics with topological classifications about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model by linear stability theory. Further, for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also studied the existence of possible bifurcations about boundary and interior equilibrium solutions and proved that there exists no flip bifurcation about boundary equilibrium solution. Moreover, it is proved that about interior equilibrium solution, there exist Hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Moreover, by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally, theoretical results are verified numerically.

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019-nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019-nCoV. We implement the forward-backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data-based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

As the first-wave COVID-19 has passed in 2020, people's awareness of self-protection began to decline gradually. How to prevent and control the second-wave COVID-19 has become an important issue in many countries and regions. By analyzing the transmission of the second-wave COVID-19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID-19 model to simulate the transmission characteristics of the second-wave COVID-19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second-wave COVID-19 in Tonghua City is , which is much smaller than that of the first-wave COVID-19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second-wave COVID-19 in other countries or regions.

For all humanity, the sudden outbreak of Corona Virus Disease 2019 has been an important problem. Timely and effective media coverage is considered to be one of the effective approaches to control the spread of epidemic in early stage. In this paper, a Sentiment-enabled Susceptible-Exposed-Infected-Recovered (SEIR) model is established to reveal the relationship between the propagation of the epidemic and media coverage. The authors take the positive and negative media coverage into consideration when implementing the Sentiment-enabled SEIR model. This model is constructed by parameterizing the number of current confirmed cases, cumulative cured cases, cumulative deaths, and media coverage. The numerical simulation and sensitivity analysis are conducted based on the Sentiment-enabled SEIR model. The numerical analysis confirms the rationality of the Sentiment-enabled SEIR model. The sensitivity analysis shows that positive media coverage acts a pivotal part in reducing the figure for confirmed cases. Negative media coverage has an effect on the figure for confirmed cases is not as significant as that of positive media coverage, but it is not negligible.

Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.

To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction number is also computed using next generation matrix method. It is shown that the model is locally stable at disease-free equilibrium point when and unstable for . The model has been analyzed for global stability at both of the disease-free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction number . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.

This is the first attempt to investigate the effects of the factors related to non-pharmaceutical interventions (NPIs) and the physical condition of the public on virulence evolution of SARS-CoV-2 and the trend of the epidemics of COVID-19 under an adaptive dynamics framework. Qualitative agreement of the prediction on the epidemics of COVID-19 with the actual situations convinced the rationality of the present model. The study showed that enhancing both NPIs (including public vigilance, quarantine measures, and hospitalization) and the physical condition of the public (including susceptibility and recovery speed) contributed to decreasing the prevalence of COVID-19 but only increasing public vigilance and decreasing the susceptibility of the public could also reduce the virulence of SARS-CoV-2. Therefore, controlling the contact rate and infection rate was the key to control not only the epidemic scale of COVID-19 but also the extent of its harm. On the other hand, the best way to control the epidemics was to increase the public vigilance and physical condition because both of them could reduce the prevalence and case fatality rate (CFR) of COVID-19. In addition, the enhancement of quarantine measures and hospitalization could bring the (slight) increase in the CFR of COVID-19.

The ongoing COVID-19 pandemic has posed a tremendous threat to the public and health authorities. Wuhan, as one of the cities experiencing the earliest COVID-19 outbreak, has successfully tackled the epidemic finally. The main reason is the implementing of Fangcang shelter hospitals, which rapidly and massively scale the health system's capacity to treat COVID-19 confirmed cases with mild symptoms. To give insights on what degree Fangcang shelter hospitals have contained COVID-19 in Wuhan, we proposed a piecewise smooth model regarding the patient triage scheme and the bed capacities of Fangcang shelter hospitals and designated hospitals. We used data on the cumulative number of confirmed cases, recovered cases, deaths, and data on the number of hospitalized individuals in Fangcang shelter hospitals and designated hospitals in Wuhan to parameterize the targeted model. Our results showed that diminishing the bed capacity or delaying the opening time of Fangcang shelter hospitals, both would result in worsening the epidemic by increasing the total number of infectives and hospitalized individuals and the effective reproduction number . The findings demonstrated that Fangcang shelter hospitals avoided 17,013 critical infections and 17,823 total infections while it saved 7 days during the process of controlling the effective reproduction number . Our study highlighted the critical role of Fangcang shelter hospitals in curbing and eventually stopping COVID-19 outbreak in Wuhan, China. These findings may provide a valuable reference for decision-makers in regarding ramping up the health system capacity to isolate groups of people with mild symptoms in areas of widespread infection.

The world has been suffering from the coronavirus disease 2019 (COVID-19) since late 2019. COVID-19 is caused by a virus called the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The human immunodeficiency virus (HIV) coinfection with SARS-CoV-2 has been reported in many patients around the world. This has raised the alarm for the importance of understanding the dynamics of coinfection and its impact on the lives of patients. As in other pandemics, mathematical modeling is one of the important tools that can help medical and experimental studies of COVID-19. In this paper, we develop a within-host SARS-CoV-2/HIV coinfection model. The model consists of six ordinary differential equations. It depicts the interactions between uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, uninfected CD4 T cells, infected CD4 T cells, and free HIV particles. We confirm that the solutions of the developed model are biologically acceptable by proving their nonnegativity and boundedness. We compute all possible steady states and derive their positivity conditions. We choose suitable Lyapunov functions to prove the global asymptotic stability of all steady states. We run some numerical simulations to enhance the global stability results. Based on our model, weak CD4 T cell immune response or low CD4 T cell counts in SARS-CoV-2/HIV coinfected patient increase the concentrations of infected epithelial cells and SARS-CoV-2 viral load. This causes the coinfected patient to suffer from severe SARS-CoV-2 infection. This result agrees with many studies which showed that HIV patients are at greater risk of suffering from severe COVID-19 when infected. More studies are needed to understand the nature of SARS-CoV-2/HIV coinfection and the role of different immune responses during infection.

The main purpose of present paper is to investigate the nonlinear model of COVID-19 (novel coronavirus) computationally. The SITR model is designed according to four classifications of Susceptible (S), Infectious (I), Treatment (T) and Recovered (R). Two convenient and effective numerical techniques namely the Adams-Bashforth Method (ABM) and Milne-Simpson Method (MSM) are employed to analyze the epidemic model. The influences of the contact rate parameter (β), recovery parameter (μ) and death parameter (α) on the variables including S, I and R are studied comprehensively. The obtained findings indicate that by increasing the contact rate parameter the infectious and recovered categories enhance but the susceptible mechanism decreases.

The coronavirus disease (COVID-19) pandemic has impacted many nations around the world. Recently, new variant of this virus has been identified that have a much higher rate of transmission. Although vaccine production and distribution are currently underway, non-pharmacological interventions are still being implemented as an important and fundamental strategy to control the spread of the virus in countries around the world. To realize and forecast the transmission dynamics of this disease, mathematical models can be very effective. Various mathematical modeling methods have been proposed to investigate the transmission patterns of this new infection. In this paper, we utilized the fractional-order dynamics of COVID-19. The goal is to control the prevalence of the disease using non-pharmacological interventions. In this paper, a novel fractional-order backstepping sliding mode control (FOBSMC) is proposed for non-pharmacological decisions. Recently, new variant of this virus have been identified that have a much higher rate of transmission, so finally the effectiveness of the proposed controller in the presence of new variant of COVID-19 is investigated.

In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic and of disease models generally. Most works follow the (SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID-19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult-to-estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems.

Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID-19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed-point theorem and by helping the Arzela-Ascoli theorem. Using the predictor-corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas.

We provide an easy and accurate method for approximating the reproduction number defined in an SIR epidemic model. At first, we present a formula extracting the exact in case of constant rates of infection and recovery assumed in an SIR model. Then, we proceed proposing an exponential fitting to various data taken from the real-world epidemics. Certain applications for current COVID outbreak are considered, and figures describing the fluctuation of in various countries are given.

In this paper, we propose a modified Susceptible-Infected-Quarantine-Recovered (mSIQR) model, for the COVID-19 pandemic. We start by proving the well-posedness of the model and then compute its reproduction number and the corresponding sensitivity indices. We discuss the values of these indices for epidemiological relevant parameters, namely, the contact rate, the proportion of unknown infectious, and the recovering rate. The mSIQR model is simulated, and the outputs are fit to COVID-19 pandemic data from several countries, including France, US, UK, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.

We formulate a simple susceptible-infectious-recovery (SIR) model to describe the spread of the coronavirus under strict social restrictions. The transmission rate in this model is exponentially decreasing with time. We find a formula for basic reproduction function and estimate the maximum number of daily infected individuals. We fit the model to induced death data in Italy, United States, Germany, France, India, Spain, and China over the period from the first reported death to August 7, 2020. We notice that the model has excellent fit to the disease death data in these countries. We estimate the model's parameters in each of these countries with 95% confidence intervals. We order the strength of social restrictions in these countries using the exponential rate. We estimate the time needed to reduce the basic reproduction function to one unit and use it to order the quality of social restrictions in these countries. The social restriction in China was the strictest and the most effective and in India was the weakest and the least effective. Policy-makers may apply the Chinese successful social restriction experiment and avoid the Indian unsuccessful one.

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.

In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.

Different countries of the world are facing a serious pandemic of corona virus disease (COVID-19). One of the most typical treatments for COVID-19 is social distancing, which includes lockdown; it will help to decrease the number of contacts for undiagnosed individuals. The main aim of this article is to construct and evaluate a fractional-order COVID-19 epidemic model with quarantine and social distancing. Laplace homotopy analysis method is used for a system of fractional differential equation (FDEs) with Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivative. By applying the ABC and Caputo derivative, the numerical solution for fractional-order COVID-19 epidemic model is achieved. The uniqueness and existence of the solution is checked by Picard-Lindelof's method. The proposed fractional model is demonstrated by numerical simulation which is useful for the government to control the spread of disease in a practical way.