key: cord-0987697-ym44blah authors: Varotsos, Costas A.; Krapivin, Vladimir F. title: A new model for the spread of COVID-19 and the improvement of safety date: 2020-08-18 journal: Saf Sci DOI: 10.1016/j.ssci.2020.104962 sha: a681af3413170c4397a36fe0883193f77c53b426 doc_id: 987697 cord_uid: ym44blah COVID-19 has been spreading rapidly around the world since December 2019. The main goal of this study is to develop a more effective method for diagnosing and predicting the COVID-19 spread and to evaluate the effectiveness of control measures to reduce and stop the virus spread. To this end, the COVID-19 Decision-Making System (CDMS) was developed to study disease transmission. CDMS divides the population into groups as susceptible, infected, cured and dead. The trends of the people’s number in these groups have deterministic and stochastic components. The deterministic components are described by a differential equations system with parameters determined by the data reported. The stochastic components are represented as an indicator of instability that characterizes the tendency of COVID-19 spread. The simulation experiments have shown a good agreement between the CDMS estimates and the data reported in Russia and Greece. The analysis performed showed that the newly-introduced instability indicator may be the precursor to the pandemic dynamics. In this context, our results showed three potential candidates for a second wave of COVID-19 disease: USA, Russia and Brazil. Although the proportion of infected individuals in countries with high temperatures is lower than in European countries and Russia, temperature and humidity are slowly affecting the effects of the pandemic. Finally, the results presented may contribute to the urgent need to reduce the risks associated with the second wave of the COVID-19, to improve public health intervention and safety measures to be taken by various countries. The mathematical tools of epidemiology, the biological models of the population, and the statistical methods allow the study of different processes of spread of the various viruses both in a restricted area and on a global scale (Brauer et al., 2012 , Freedman, 2012 , Krapivin et al., 2015 , Xue et al., 2014 . Specifically, mathematical methods are used in microbiology and virology to detect important factors that control the spread of the virus. Traditionally, a mathematical model has been able to predict the evolution of the virus between different regions, which is the focus of the World Health Organization (WHO), mainly for some West African countries. For example, a forecasting of the progression of the epidemic with a deadly human disease was made for the Ebola virus disease discovered in 1976 in Central Africa. In this case, the spread of the Ebola virus was limited to two areas including Zaire and Sudan, which did not require global efforts to reduce its spread to other areas. Understanding the pathways of any virus transmission is usually achieved by using different mathematical models adapted to the epidemiological parameters of the specific virus. The situation with coronavirus differs significantly from other events in recent decades. Global panic erupted in early December 2019 when the first victim of COVID-19 was diagnosed in Wuhan, China. After that, the number of infected people in many countries increased rapidly. Most governments have begun to introduce restrictions on human mobility inside and outside their countries in order to reduce the spread of the virus. In particular, these restrictions, which were intended to reduce and eliminate the spread of the coronavirus, include, among others things:  restrictions of international and domestic flights,  prohibition of population concentration in groups,  defining different marketing processes,  transition to remote working regime,  establishment a self-isolation regime for many groups of the human population (social distancing),  use quarantine regime and isolate individuals or their groups considered to be suspected carriers of the virus, and  introduction of financial support measures for various sectors of the national economy. However, the situation with COVID-19 differs significantly from the pandemic cases in the past, both in the very high rate of global spread and in the dramatic increase in infected and diseased people and in the absence of a vaccine against this virus. Therefore, epidemic models developed in time helped to understand the role of different quarantine parameters. The existing mathematical models that were able to adapt to the short-term forecasts of stochastic processes that govern the COVID-19 pandemic , Karako et al., 2020 , Plank et al., 2020 , Tiwari, 2020 offered great help in this. Most of these models use differential equations systems, some parameters of which reflect the characteristics of the COVID-19 pandemic process. He et al. (2020) developed a discrete-time stochastic epidemic model from which relevant parameters were estimated using statistical data from January 11 to February13, 2020 in China. Plank et al. (2020) based on a continuous-time branching process model, considered different scenarios to isolate the cases and assessed the effects of restrictive control on the population of New Zealand. Tiwary (2020) evaluated the effectiveness of the Susceptible-Infected-Removed (SIR) and Susceptible-Infectious-Quarantined-Recovered (SIQR) models for reducing COVID-19 spread using personal isolation and has defined parameters and indicators that quantify the COVID-19 spread in India. Karako et al. (2020) using the stochastic transmission model, assessed the effectiveness of the strategies for controlling the spread of COVID-19 in Japan. Analyzing the cases in China, proposed a timeindependent susceptible-infected-recovered model that can be used to predict the number of infected and dead. This model is based on two time-invariant variables that reflect an individual's average contacts with others per unit time and the recovery rate. The present study develops the method of predicting the spread of COVID-19 by examining various scenarios depending on the range of people movements and interactions , Krapivin, 1970 , Krapivin and Mkrtchyan, 2019 . The COVID-19 decisionmaking system (CDMS) is designed to assess epidemic parameters and predict the epidemic consequences. The epidemic situation in many countries at the beginning of COVID-19 infection was shaped by different social restrictions and medical events which, as a rule, were determined on the basis of specialized solutions, the effectiveness of which depends significantly on the use of technology for big data processing and management (Chattopadhyay et al., 2012 , Kwon et al., 2020 , Varotsos et al., 2017 . CDMS divides the population into groups of individuals as susceptible (S (t)), infected (P(t)), recovered (R(t)), and dead (D(t)). The overall size of the population is N. The interactions between groups are described by the following equations that reflect the dependence of individuals' health on different management parameters, such as quarantine establishment and traffic restrictions. (1) where t is the running time, t is the operational time interval, (t) is the probability of transition in time t,  is the immune indicator, (t) is the recovering rate in time t, (t) is the death rate caused by the disease, q(t) is the indicator of medical support, I(t) is the instability indicator of stochastic component. The numerical evaluations of the parameters in (1) are carried out by the SARD block using statistical reports on the status of the effects of COVID-19 disease. Using the reported data, the following parameters can be calculated (Chen, Y.C et al., 2020 , Chen S et al., 2020 : All processes caused by COVID-19 have a stochastic component, the stability of which characterizes the level of uncertainty in the observed data and helps to forecast the epidemic characteristics more accurately. The indicator instability (I(t)) indicates the phase state of the components Y(t)={S(t), P(t), R(t), D(t)} (Kondratyev et al., 2006, Varotsos and Krapivin, 2017) : where n is the time interval for the mean of the parameters, m is the start time for data input, s is the number of characteristics registered, b i [0.1] is the update value of the i-th characteristic, An indicator I(t) defined by Eqs. The migration processes of any virus have probabilistic and deterministic components that determine the rate of loss of income due to the virus pandemic. CDMS describes the transient processes that occurred in 2020 in many parts of the world. Epidemiology theory provides an interdisciplinary approach to disease transmission processes (Anderson, 1979 , Diekmann et al., 2012 , Oldstone, 2009 , Omran, 2005 . The methodological approach to the COVID-19 spread conducted at CDMS is based on the use of differential equations and stochastic methods to simulate transition processes between population phase states, such as susceptible, exposed, infected, hospitalized, recovered, and died ( He et al., 2020) . The transition of an individual between his states is considered a stochastic process with the Wald distribution (Krapivin, 1970 , Wald, 1947 . The movement of the population within the given area is controlled by the restrictions introduced by the administration and is followed by reported and simulated data, and then the consequences of COVID-19 disease depend mainly on these restrictions. Different countries use almost identical set of restrictions such as self-isolation, quarantine, testing, social distancing, hospitalization (ICAO, 2020), which are characterized by various parameters. pandemic on climate (Fuentes et al., 2020 , Wang et al., 2020 . The analysis of global pandemic data allows the preliminary conclusion that temperature and humidity slowly affect the effects of pandemic. The rate of infected people in countries with high temperatures is lower than in European countries and Russia. The stages of spread and the rate of loss of income due to the pandemic COVID-19 2020 have different overwhelming results essentially not depending on the region, but as shown in Fig. 2 , there is a correlation between infected and dead people. With the increase in infected people, the number of dead income has stabilized regardless of time. The number of infected people in Russia includes 10% of those infected in Moscow. An analysis of traffic restrictions introduced during the pandemic, which began in Russia more than 2 months after the Moscow shutdown, shows that the problem of returning tourists to Russia has been solved by a non-optimal method. Travelers arriving in Moscow from other countries are tested and if some are diagnosed with coronavirus are self-isolated at home or hospitalized if they have severe symptoms. The tactics of self-isolation at home of confirmed individuals with coronavirus is not optimal. Figure 4 shows the modeling results when 50% of travelers arriving in Moscow could be isolated immediately in two weeks (Scenario 1 rus ). The 2 rus scenario corresponds to 100% isolation of travelers. Table 2 . results that showed the possibility of a combined use of a model and statistical data analysis to assess the pandemic effects on the population. This study used data reported from 11 January to 30 June 2020. The newly-introduced instability indicator I(t) describes trends in the number of susceptible S(t), infected P(t), recovered R(t) and dead D(t) individuals. The maximum value of I(t) corresponds to the maximum of these functions. Preliminary analysis of simulation experiments using CDMS shows that the arrival situation when I(t) begins to increase after reduction can be interpreted as the beginning of the second wave of COVID-19. Unfortunately, there is not enough data to make this study reliable. The data in Table 3 can only be indicative of the possible presence of a coronavirus outbreak in another phase, which is interpreted as a "second wave". The results of Table 3 allow the separation of three candidates for the second wave -the USA, Russia and Brazil. The probability of the coronavirus pandemic to pass into a negative phase is equal to 0.460.08 for USA, 0.370.06 for Russia and 0.420.07 for Brazil. In particular, the calculation of I(t) for the reported data on the pandemic income recorded during a week helps to estimate this probability for all countries or other restricted areas. It is clear that protection measures in different countries are not effective enough and could be more effective in the future to analyze more data using different models, such as the stochastic model SEIR (Susceptible, Exposed, Infectious, Recovered) and the susceptibleinfected-deceased (SID) model ( He et al., 2020 , Islam et al., 2020 . The existence of reserves in social and economic measures is followed by the comparison of relations P(t)/S(t), R(t)/P(t), and D(t)/P(t) for different countries where the dynamic variations of these indicators can achieve more than 50%. In practice, it was impossible to coordinate measures to curb the pandemic of COVID-19 in conditions of high uncertainty. Therefore, in this study the decision-making system can be modernized to take into account the results of COVID-19 pandemic, taking into account the overall social, medical and administrative resources that can be used to minimize economic and population losses. The issue of validating the CDMS is resolved by data shown in Figures 4 and 5 , where the deviation of the model results from the reported data is evaluated by 8.5% for Russia and 1.6% for Greece. The rate of a dramatic increase in the reported cases in many countries depends on the big data generated by a complex task of modernized CDMS validation, taking into account the uncertainty levels in the data provided by administration of countries and the World Health Organization (Ivorra, 2020 , Park et al., 2020 . In this area the results of the present study mentioned above clearly provide the potential for improved safety. 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