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• New COVID-19 mathematical model with lock-down effect. • New fractal-fractional differentiation. • New fractal-fractional integration. • Numerical scheme based on Newton polynomial. Countries around the world are implementing lock-down measures in a bid to flatten the curve of the new deadly COVID-19 disease. Our paper does not claim to have found the cure for COVID-19, neither does it claim that the suggested model have taken into account all the complexities around the spread of the disease. Nonetheless, the fundamental question asked in this paper is to know if within the conditions taken into account in this suggested model, the integral lock-down is effective in saving human lives. To answer this question, a mathematical model was suggested taking into account the possibility of transmission of COVID-19 from dead bodies to humans and the effect of lock-down. Three cases were considered. The first case suggested that there is transmission from dead to the living (medical staffs as they perform postmortem procedures on corpses, and direct contacts with during burial ceremonies). This case has no equilibrium points except for disease free equilibrium, a clear indication that care must be taken when dealing with corpses due to corona-19. In the second case we removed the transmission rate from dead bodies. This case showed an equilibrium point, although the number of deaths, carriers and infected grew exponentially up to a certain stability level. In the last case, we incorporated a lock-down and social distancing effect, using the next generation matrix. We could achieve a zero reproduction number, with number of deaths, infected and carriers decaying very rapidly. This is a clear indication that if lock-down recommendations are observed the threat of COVID-19 can be reduced to zero in few months.While our mathematical model agrees with the effectiveness of the lock-down, it is important to mention damaging effects of inadequate testing. The long waiting period of few days before confirmation of status, can only lead to more infections. The asymptomatic tested person could be positive and spread the infection, or could contact the virus in days after testing and will spread the disease further, after being given a false result. Testing kit that with immediate results are needed for more efficient measures. We used Italy's Data to guide the construction of the mathematical model. To include non-locality into mathematical formulas, differential and integral operators were suggested. Properties and numerical approximations were presented in details. Finally, the suggested differential and integral operators were applied to the model. [ABSTRACT FROM AUTHOR]

• Z-control approach is applied on a SEIR model with an overexposure mechanism. • Awareness is considered as an indirect control on the class of infective individuals. • Z-control is used to detect what trend must awareness display to eradicate the disease. • The Z-procedure is generalized to treat high-dimensional uncontrolled models. • The awareness variable is qualitatively compared to Google Trends data on Covid19. In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic. [ABSTRACT FROM AUTHOR]

• Developed deep learning methods to forecast the COVID19 spread. • Five deep learning models have been compared for COVID-19 forecasting. • Time-series COVID19 data from Italy, Spain, France, China, the USA, and Australia are used. • Results demonstrate the potential of deep learning models to forecast COVID19 data. • Results show the superior performance of the Variational AutoEncoder model. The novel coronavirus (COVID-19) has significantly spread over the world and comes up with new challenges to the research community. Although governments imposing numerous containment and social distancing measures, the need for the healthcare systems has dramatically increased and the effective management of infected patients becomes a challenging problem for hospitals. Thus, accurate short-term forecasting of the number of new contaminated and recovered cases is crucial for optimizing the available resources and arresting or slowing down the progression of such diseases. Recently, deep learning models demonstrated important improvements when handling time-series data in different applications. This paper presents a comparative study of five deep learning methods to forecast the number of new cases and recovered cases. Specifically, simple Recurrent Neural Network (RNN), Long short-term memory (LSTM), Bidirectional LSTM (BiLSTM), Gated recurrent units (GRUs) and Variational AutoEncoder (VAE) algorithms have been applied for global forecasting of COVID-19 cases based on a small volume of data. This study is based on daily confirmed and recovered cases collected from six countries namely Italy, Spain, France, China, USA, and Australia. Results demonstrate the promising potential of the deep learning model in forecasting COVID-19 cases and highlight the superior performance of the VAE compared to the other algorithms. [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]