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• This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. • This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. • A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. • An extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread. [ABSTRACT FROM AUTHOR]

• Giving a new model of coronavirus epidemic outbreak considering quarantined individuals. • Optimal controller design. • Parallel control design consisting of antiviral treatment and quarantine strategy. • Evaluate suddenly increased in population as an impulsive epidemic model of SQEIAR. • Comparison of the controller results for three types of diseases (COVID-19, Ebola, and, Influenza). • Evaluation of the controller with system parameters identified using actual data. This paper presents a SEIAR-type model considering quarantined individuals (Q), called SQEIAR model. The dynamic of SQEIAR model is defined by six ordinary differential equations that describe the numbers of Susceptible, Quarantined, Exposed, Infected, Asymptomatic, and Recovered individuals. The goal of this paper is to reduce the size of susceptible, infected, exposed and asymptomatic groups to consequently eradicate the infection by using two actions: the quarantine and the treatment of infected people. To reach this purpose, optimal control theory is presented to control the epidemic model over free terminal optimal time control with an optimal cost. Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. Also, an impulsive epidemic model of SQEIAR is considered to deal with the potential suddenly increased in population caused by immigration or travel. Since this model is suitable to describe the COVID-19 pandemic, especial attention is devoted to this case. Thus, numerical simulations are given to prove the accuracy of the theoretical claims and applied to the particular data of this infection. Moreover, numerical computations of the COVID-19 are compared with diseases like Ebola and Influenza. In addition, the controller is evaluated with system parameters identified by using actual data of China. Finally, the controller tuned with the estimated parameters of the Chinese data is applied to the actual data of Spain to compare the quarantine and treatment policies in both countries. [ABSTRACT FROM AUTHOR]

• For the first time, we have incorporated the temporal-spatial heterogeneous environment, Time delay, home quarantine and relapse factors into the study of mathematical epidemic models. We have innovatively constructed a time delay reaction-diffusion COVID-19 epidemic model with home quarantine and relapse in the temporal-spatial heterogeneous environment. • We use the global exponential attractor theory to discuss the global dynamic behavior of the model, which overcomes the failure of the commonly used method to prove global stability due to the increase in the number of equations and the increased coupling between equations. • Combine with the official data of the COVID-19 and the national control strategy, some numerical simulations on the stability and global exponential attractiveness of the COVID-19 epidemic in China and the USA are given. The simulation results fully reflect the impact of the temporalspatial heterogeneous environment, relapse, time delay and home quarantine strategies on the spread of the epidemic, revealing the significant differences in epidemic prevention strategies and control effects between the East and theWest. The results of this study provide a theoretical basis for the current epidemic prevention and control. As the COVID-19 epidemic has entered the normalization stage, the task of prevention and control remains very arduous. This paper constructs a time delay reaction-diffusion model that is closer to the actual spread of the COVID-19 epidemic, including relapse, time delay, home quarantine and temporal-spatial heterogeneous environment that affect the spread of COVID-19. These factors increase the number of equations and the coupling between equations in the system, making it difficult to apply the methods commonly used to discuss global dynamics, such as the Lyapunov function method. Therefore, we use the global exponential attractor theory in the infinite-dimensional dynamic system to study the spreading trend of the COVID-9 epidemic with relapse, time delay, home quarantine in a temporal-spatial heterogeneous environment. Using our latest results of global exponential attractor theory, the global asymptotic stability and the persistence of the COVID-19 epidemic are discussed. We find that due to the influence of relapse in the in temporal-spatial heterogeneity environment, the principal eigenvalue λ * can describe the spread of the epidemic more accurately than the usual basic reproduction number R 0. That is, the non-constant disease-free equilibrium is globally asymptotically stable when λ * < 0 and the COVID-19 epidemic is persisting uniformly when λ * > 0. Combine with the latest official data of the COVID-19 and the prevention and control strategies of different countries, some numerical simulations on the stability and global exponential attractiveness of the spread of the COVID-19 epidemic in China and the USA are given. The simulation results fully reflect the impact of the temporal-spatial heterogeneous environment, relapse, time delay and home quarantine strategies on the spread of the epidemic, revealing the significant differences in epidemic prevention strategies and control effects between the East and the West. The results of this study provide a theoretical basis for the current epidemic prevention and control. [ABSTRACT FROM AUTHOR]

Coronavirus genomic infection-2019 (COVID-19) has been announced as a serious health emergency arising international awareness due to its spread to 201 countries at present. In the month of April of the year 2020, it has certainly taken the pandemic outbreak of approximately 11,16,643 infections confirmed leading to around 59,170 deaths have been recorded world-over. This article studies multiple countries-based pandemic spread for the development of the COVID-19 originated in the China. This paper focuses on forecasting via real-time responses data to inherit an idea about the increase and maximum number of virus-infected cases for the various regions. In addition, it will help to understand the panic that surrounds this nCoV-19 for some intensely affecting states possessing different important demographic characteristics that would be affecting the disease characteristics. This study aims at developing soft-computing hybrid models for calculating the transmissibility of this genome viral. The analysis aids the study of the outbreak of this virus towards the other parts of the continent and the world. A hybrid of wavelet decomposed data into approximations and details then trained & tested through neuronal-fuzzification approach. Wavelet-based forecasting model predicts for shorter time span such as five to ten days advanced number of confirmed, death and recovered cases of China, India and USA. While data-based prediction through interpolation applied through moving average predicts for longer time spans such as 50–60 days ahead with lesser accuracy as compared to that of wavelet-based hybrids. Based on the simulations, the significance level (alpha) ranges from 0.10 to 0.67, MASE varying from 0.06 to 5.76, sMAPE ranges from 0.15 to 1.97, MAE varies from 22.59 to 6024.76, RMSE shows a variation from 3.18 to 8360.29 & R2 varying through 0.0018 to 0.7149. MASE and sMAPE are relatively lesser applied and novel measures that aimed to achieve increase in accuracy. They eliminated skewness and made the model outlier-free. Estimates of the awaited outburst for regions in this study are India, China and the USA that will help in the improvement of apportionment of healthcare facilities as it can act as an early-warning system for government policy-makers. Thus, data-driven analysis will provide deep insights into the study of transmission of this viral genome estimation towards immensely affected countries. Also, the study with the help of transmission concern aims to eradicate the panic and stigma that has spread like wildfire and has become a significant part of this pandemic in these times. [ABSTRACT FROM AUTHOR]

• The very first model to predict the minimum optimal time of the lockdown. • Deliberates salient features like silent carriers, sociability of newly infected person and unregistered deaths of coronavirus infectious people along with SIR model. • Based on the awareness and sustainability of disease, the number of suspected person varies with respect to time of spreading of virus. Hence, three phases are formed to define the suspected rate as it will not grow exponentially all the time. • At first Phase, when the awareness of newly discovered virus is at initial phases, the suspecting rate will grow exponentially. Suspected rate depends on sociability of infected person. • Second Phase is during lockdown when the social distancing is followed. In this phase, death cases are more as number of current infected person are at peak. Simultaneously, the number of recovered person per day will increase. • Third Phase is when there is reduction in number of active cases. Number of suspected cases will reduce depending upon the testing speed of medical team. • In order to calculate the optimal lockdown time T opt , the approach of proposed model is to find a situation when the number suspected people starts to reduce w.r.t. time, number of infected people increases for a while but start reducing with respect to time, and also the number of recovered people rises w.r.t. time. • The model is tested on China data and is efficient enough to propose a model very close to their actual figures of infected people, recovered people, died and active cases. The model predicts the optimal lockdown period as 73 days for China which is very close to their actual lockdown period (77 days). • Also, the model is implemented to predict the optimal lockdown period of India and Italy. • The programming part is done in C++ language with Linux OS. This paper proposes a three-phase Susceptible-Infected-Recovered-Dead (3P-SIRD) model to calculate an optimal lockdown period for some specific geographical regions that will be favorable to break not only the transmission chain but also will help country's economy to recover and support infrastructure in a fight against COVID-19. Proposed model is novel since it additionally includes parameters i.e. silent carriers, sociability of newly infected person and unregistered died coronavirus infected people along with the infection rate, suspected rate and death rate. These parameters contribute a lot to figure out the more clear model, along with essential parameters. The model takes the testing rate of suspected people into consideration and this rate varies with respect to phase of the epidemic growth. Proposed 3P-SIRD model is divided into three-phases based on the awareness and sustainability of disease. Time is divided into different periods as rate of infection and recovery fluctuates region to region. The model is tested on China data and is efficient enough to propose a model very close to their actual figures of infected people, recovered people, died and active cases. The model predicts the optimal lockdown period as 73 days for China which is very close to their actual lockdown period (77 days). Further, the model is implemented to predict the optimal lockdown period of India and Italy. [ABSTRACT FROM AUTHOR]