Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy.
TL;DR: In this article, the dynamics of a COVID-19 stochastic model with isolation strategy were investigated, and the existence and uniqueness of a global positive solution were proven, and stochastically dynamic properties of the stochnastic solution around the deterministic model equilibria were investigated.
Abstract: This paper investigates the dynamics of a COVID-19 stochastic model with isolation strategy. The white noise as well as the Levy jump perturbations are incorporated in all compartments of the suggested model. First, the existence and uniqueness of a global positive solution are proven. Next, the stochastic dynamic properties of the stochastic solution around the deterministic model equilibria are investigated. Finally, the theoretical results are reinforced by some numerical simulations.
Citations
More filters
TL;DR: In this article , a generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine, and an efficient numerical technique is applied to simulate the new model and provide the associated numerical results.
Abstract: A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.
115 citations
TL;DR: In this article, a generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine, and an efficient numerical technique is applied to simulate the new model and provide the associated numerical results.
Abstract: A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R 0 ≈ 6.6361 . Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.
115 citations
TL;DR: In this article, the authors evaluated the performance of three deep learning methods and their bidirectional extensions to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days.
Abstract: The first known case of Coronavirus disease 2019 (COVID-19) was identified in December 2019. It has spread worldwide, leading to an ongoing pandemic, imposed restrictions and costs to many countries. Predicting the number of new cases and deaths during this period can be a useful step in predicting the costs and facilities required in the future. The purpose of this study is to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days. The motivation for predicting every n days (instead of just every day) is the investigation of the possibility of computational cost reduction and still achieving reasonable performance. Such a scenario may be encountered in real-time forecasting of time series. Six different deep learning methods are examined on the data adopted from the WHO website. Three methods are LSTM, Convolutional LSTM, and GRU. The bidirectional extension is then considered for each method to forecast the rate of new cases and new deaths in Australia and Iran countries. This study is novel as it carries out a comprehensive evaluation of the aforementioned three deep learning methods and their bidirectional extensions to perform prediction on COVID-19 new cases and new death rate time series. To the best of our knowledge, this is the first time that Bi-GRU and Bi-Conv-LSTM models are used for prediction on COVID-19 new cases and new deaths time series. The evaluation of the methods is presented in the form of graphs and Friedman statistical test. The results show that the bidirectional models have lower errors than other models. A several error evaluation metrics are presented to compare all models, and finally, the superiority of bidirectional methods is determined. This research could be useful for organisations working against COVID-19 and determining their long-term plans.
65 citations
TL;DR: In this paper, the population dynamics model including the predator-prey problem and the logistic equation are generalized by using fractional operator in term of Caputo-Fabrizio derivative (CF-derivative).
Abstract: In this research, the population dynamics model including the predator-prey problem and the logistic equation are generalized by using fractional operator in term of Caputo-Fabrizio derivative (CF-derivative). The models under study include of fractional Lotka-Volterra model (FLVM), fractional predator-prey model (FPPM) and fractional logistic model of population growth (FLM-PG) with variable coefficients. After that a numerical scheme is presented to obtain numerical solutions of these fractional models. These solutions are made using three-step Adams-Bashforth scheme. To show the efficiency and the accuracy of the present scheme, a few examples are evaluated. The numerical simulations of the results are depicted the accuracy of the present scheme.
36 citations
TL;DR: A piecewise numerical approach is presented to derive numerical solutions of piecewise modeling models and is concluded that this concept is a new window that will help mankind to better understand nature.
Abstract: Several collected data representing the spread of some infectious diseases have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish flu and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns, a clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely. The idea was first applied in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature.
35 citations
References
More filters
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
Abstract: (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
8,238 citations
TL;DR: The findings are consistent with person-to-person transmission of this novel coronavirus in hospital and family settings, and the reports of infected travellers in other geographical regions.
7,392 citations
TL;DR: This study describes possible transmission of novel coronavirus disease 2019 (COVID-19) from an asymptomatic Wuhan resident to 5 family members in Anyang, a Chinese city in the neighboring province of Hubei.
Abstract: This study describes possible transmission of novel coronavirus disease 2019 (COVID-19) from an asymptomatic Wuhan resident to 5 family members in Anyang, a Chinese city in the neighboring province of Hubei.
3,818 citations
TL;DR: The WHO–UNICEF–Lancet Commission presents a candid assessment of the threats children face and the sombre implications for their future, and emphasises the role of community engagement in promoting the health and development of the world’s children.
830 citations
TL;DR: In this paper, the authors quantified expression noise from the long terminal repeat (LTR) promoter at different HIV-1 integration sites across the human genome and found that the measured noise levels are inconsistent with constitutive gene expression models, and that each burst generates an average of 2-10 mRNA transcripts before the promoter returned to an inactive state.
241 citations