Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy.

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.

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.

Abstract: In this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a solution for this model, a numerical technique is presented which is based on operational matrix. First, we assume the solution of the problem under the study is as an expansion of the Bernoulli polynomials. Then with combination of the operational matrix based on the Bernoulli polynomials and collocation method, the problem under the study is changed to a system of nonlinear algebraic equations. Finally, the proposed technique is simulated and tested on three types of the FBEs to confirm the superiority and accuracy.

Abstract: In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.

Abstract: A probabilistic method is proposed in this study to predict the spreading profile of the coronavirus disease 2019 (COVID-19) in the United State (US) via time-variant reliability analysis. To this end, an extended susceptible-exposed-infected-vaccinated-recovered (SEIVR) epidemic model is first established deterministically, considering the quarantine and vaccination effects, and then applied to the available COVID-19 data from US. Afterwards, the prediction results are described as a time-series of the number of people infected, recovered, and dead. Upon introducing the extended SEIVR model into a limit-state function and defining the model parameters including transmission, recovery, and mortality rates as random variables, the problem is transformed into a reliability model and analyzed by the Monte Carlo sampling. The findings are subsequently given in the form of exceedance probabilities (EPs) of the three main outputs, namely, the maximum number of infected cases, the total number of recovered cases, and the total number of fatal cases. Afterwards, by incorporating time into the formulation of the reliability problem, the EPs are calculated over time and presented as 3D probability graphs, illustrating the relationship between the number of cases affected (i.e., infected, recovered, or dead), exceedance probability, and time. The results for the US demonstrate that, by the end of 2021, the number of the infected (active) cases decreases to 0.8 million and number of cases recovered and fatalities increases to 41.3 million and 0.6 million, respectively.

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.

Abstract: Summary Background An ongoing outbreak of pneumonia associated with a novel coronavirus was reported in Wuhan city, Hubei province, China. Affected patients were geographically linked with a local wet market as a potential source. No data on person-to-person or nosocomial transmission have been published to date. Methods In this study, we report the epidemiological, clinical, laboratory, radiological, and microbiological findings of five patients in a family cluster who presented with unexplained pneumonia after returning to Shenzhen, Guangdong province, China, after a visit to Wuhan, and an additional family member who did not travel to Wuhan. Phylogenetic analysis of genetic sequences from these patients were done. Findings From Jan 10, 2020, we enrolled a family of six patients who travelled to Wuhan from Shenzhen between Dec 29, 2019 and Jan 4, 2020. Of six family members who travelled to Wuhan, five were identified as infected with the novel coronavirus. Additionally, one family member, who did not travel to Wuhan, became infected with the virus after several days of contact with four of the family members. None of the family members had contacts with Wuhan markets or animals, although two had visited a Wuhan hospital. Five family members (aged 36–66 years) presented with fever, upper or lower respiratory tract symptoms, or diarrhoea, or a combination of these 3–6 days after exposure. They presented to our hospital (The University of Hong Kong-Shenzhen Hospital, Shenzhen) 6–10 days after symptom onset. They and one asymptomatic child (aged 10 years) had radiological ground-glass lung opacities. Older patients (aged >60 years) had more systemic symptoms, extensive radiological ground-glass lung changes, lymphopenia, thrombocytopenia, and increased C-reactive protein and lactate dehydrogenase levels. The nasopharyngeal or throat swabs of these six patients were negative for known respiratory microbes by point-of-care multiplex RT-PCR, but five patients (four adults and the child) were RT-PCR positive for genes encoding the internal RNA-dependent RNA polymerase and surface Spike protein of this novel coronavirus, which were confirmed by Sanger sequencing. Phylogenetic analysis of these five patients' RT-PCR amplicons and two full genomes by next-generation sequencing showed that this is a novel coronavirus, which is closest to the bat severe acute respiatory syndrome (SARS)-related coronaviruses found in Chinese horseshoe bats. Interpretation Our 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. Funding The Shaw Foundation Hong Kong, Michael Seak-Kan Tong, Respiratory Viral Research Foundation Limited, Hui Ming, Hui Hoy and Chow Sin Lan Charity Fund Limited, Marina Man-Wai Lee, the Hong Kong Hainan Commercial Association South China Microbiology Research Fund, Sanming Project of Medicine (Shenzhen), and High Level-Hospital Program (Guangdong Health Commission).

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.

Abstract: 542 www.thelancet.com Vol 395 February 22, 2020 The WHO Scientific and Technical Advisory Group for Infectious Hazards (STAG-IH), working with the WHO secretariat, reviewed available information about the outbreaks of 2019 novel coronavirus disease (COVID-19) on Feb 7, 2020, in Geneva, Switzerland, and concluded that the continuing strategy of containment for elimination should continue, and that the coming 2–3 weeks through to the end of February, 2020, will be crucial to monitor the situation of community transmission to update WHO public health recommendations if required. Genetic analysis early in the outbreak of COVID-19 in China revealed that the virus was similar to, but distinct from, severe acute respiratory syndrome coronavirus (SARS-CoV), but the closest genetic similarity was found in a coronavirus that had been COVID-19: what is next for public health? U-Report to identify how and where young people wish to be involved in advancing the goal of promoting mental health and wellbeing in their communities and wider society. Alongside scalability, a need exists for inclusive tools that allow for genuine and meaningful engagement from children in rural areas, ethnic minorities, gender and sexual minorities, those exposed to poverty and violence, and those who experience health challenges. In our work with the Lancet Commission on Global Mental Health and Sustainable Development on the My Mind Our Humanity campaign, arts-based approaches have allowed us to engage young people from a range of backgrounds, both face-to-face and online. Poetry and music have created safe spaces for sharing deeply personal experiences of mental health challenges and supporting each other. These approaches have allowed us to challenge stigma by reminding young people of our shared humanity. The potential of artsbased and digital tools to foster inclusive engagement and participation is important, and our capacity to empower young generations is dependent on our ability to harness these and other resources to understand their values and experiences. The WHO–UNICEF–Lancet Commission invites us to think holistically about children and their rights to be heard and respected, and emphasises the role of community engagement in promoting the health and development of the world’s children. Children’s participation goes far beyond formal, high-level platforms. Having a voice—or lacking one—defines every relationship and interaction children experience at home and in school, work, leisure settings, and other spaces they inhabit. Children are empowered when they feel safe and welcome at home and school; when they have someone to talk to if something is wrong; and when family, friends, and teachers hear their concerns and appreciate their ideas. Indeed, family togetherness and connection to one’s culture are crucial for health and wellbeing, according to the children consulted by the Commission, from communities across New Zealand, Lebanon, Nigeria, and Argentina. The potential of shared experiences to harness children’s health and wellbeing is enormous. By fostering a culture of connectedness and mutual respect, we meet children’s needs for self-esteem and confidence and strengthen their ability to make a difference. The WHO–UNICEF–Lancet Commission presents a candid assessment of the threats children face and the sombre implications for their future. But the Commission also presents a clear vision for making a better world, for them and with them. Too often have we seen young people sidelined while those who have the power to make a change hesitate. For too long have young people been silenced, mocked, and judged for their bold ambitions to challenge the status quo. We will not be deterred. Now and always, the voices of children will call for an inclusive, fair, and sustainable future.

Abstract: Analysis of noise in gene expression has proven a powerful approach for analyzing gene regulatory architecture. To probe the regulatory mechanisms controlling expression of HIV-1, we analyze noise in gene-expression from HIV-1's long terminal repeat (LTR) promoter at different HIV-1 integration sites across the human genome. Flow cytometry analysis of GFP expression from the HIV-1 LTR shows high variability (noise) at each integration site. Notably, the measured noise levels are inconsistent with constitutive gene expression models. Instead, quantification of expression noise indicates that HIV-1 gene expression occurs through randomly timed bursts of activity from the LTR and that each burst generates an average of 2-10 mRNA transcripts before the promoter returns to an inactive state. These data indicate that transcriptional bursting can generate high variability in HIV-1 early gene products, which may critically influence the viral fate-decision between active replication and proviral latency.