New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system
TL;DR: The obtained results show the effectiveness of the theoretical method considered for the governing system, and present much light on the dynamic behavior of the Bats-Hosts-Reservoir-People transmission network coronavirus model.
Abstract: According to the report presented by the World Health Organization, a new member of viruses, namely, coronavirus, shortly 2019-nCoV, which arised in Wuhan, China, on January 7, 2020, has been introduced to the literature. The main aim of this paper is investigating and finding the optimal values for better understanding the mathematical model of the transfer of 2019-nCoV from the reservoir to people. This model, named Bats-Hosts-Reservoir-People coronavirus (BHRPC) model, is based on bats as essential animal beings. By using a powerful numerical method we obtain simulations of its spreading under suitably chosen parameters. Whereas the obtained results show the effectiveness of the theoretical method considered for the governing system, the results also present much light on the dynamic behavior of the Bats-Hosts-Reservoir-People transmission network coronavirus model.
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TL;DR: In this paper, a modified SEIR compartmental model accounting for the spread of infection during the latent period, in which they also incorporate effects of varying proportions of containment, was applied to evaluate the confinement rate at the first stages of the epidemic outbreak in order to assess the scenarios that minimize the incidence but also the mortality.
Abstract: After the spread of the SARS-CoV-2 epidemic out of China, evolution in the pandemic worldwide shows dramatic differences among countries. In Europe, the situation of Italy first and later Spain has generated great concen, and despite other countries show better prospects, large uncertainties yet remain on the future evolution and the efficacy of containment, mitigation, or attack strategies. This Manuscript was originally written in the last days of March as a way to report on the first current wave of the pandemic. The results were updated several times for March and also for the month of July. Here we applied a modified SEIR compartmental model accounting for the spread of infection during the latent period, in which we also incorporate effects of varying proportions of containment. We fit data to reported infected populations at the beginning of the first peak of the pandemic to account for the uncertainties in case reporting and study the scenario projections for the individual regions (CCAA). The aim of this model it’s to evaluate the confinement rate at the first stages of the epidemic outbreak in order to assess the scenarios that minimize the incidence but also the mortality. Results indicate that with data for March 23, the epidemics follow an evolution similar to the isolation of 1 , 5 percent of the population, and if there were no effects of intervention actions it might reach a maximum of over 1.4 M infected around April 27. The effect on the epidemics of the ongoing partial confinement measures is yet unknown (an update of results with data until March 31st is included), but increasing the isolation around ten times more could drastically reduce the peak to over 100 k cases by early April, while each day of delay in taking this hard containment scenario represents a 90 percent increase of the infected population at the peak. Dynamics at the sub aggregated levels of CCAA show epidemics at the different levels of progression with the most worrying situation in Madrid and Catalonia. Increasing alpha values up to 10 times, in addition to a drastic reduction in clinical cases, would also more than a half the number of deaths. Updates for March 31st simulations indicate a substantial reduction in burden is underway. A similar approach conducted for Italy pre-and post-intervention also begins to suggest a substantial reduction in both infected and deaths has been achieved, showing the efficacy of drastic social distancing interventions. By last we show the real evolution of the pandemic up to the end of May and the beginning of July in order to calculate the real confinement rate from data to compare with the scenarios formulated at March.
186 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., 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
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Qun Li1, Xuhua Guan1, Peng Wu2, Xiaoye Wang1, Lei Zhou1, Yeqing Tong1, Ruiqi Ren1, Kathy Leung2, Eric H. Y. Lau2, Jessica Y. Wong2, Xuesen Xing1, Nijuan Xiang1, Yang Wu1, Chao Li1, Chen Qi1, Dan Li1, Tian Liu1, Jing Zhao1, Man Liu1, Wenxiao Tu1, Chuding Chen1, Lianmei Jin1, Rui Yang1, Qi Wang1, Suhua Zhou1, Rui Wang1, Hui Liu1, Yingbo Luo1, Yuan Liu1, Ge Shao1, Huan Li1, Zhongfa Tao1, Yang Yang3, Yang Yang4, Zhiqiang Deng5, Boxi Liu5, Zhitao Ma5, Yanping Zhang1, Guoqing Shi1, Tommy Tsan-Yuk Lam2, Joseph T. Wu2, George F. Gao6, George F. Gao1, Benjamin J. Cowling2, Bo Yang5, Gabriel M. Leung2, Zijian Feng1 •
TL;DR: There is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019 and considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere.
Abstract: Background The initial cases of novel coronavirus (2019-nCoV)–infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the...
13,101 citations
"New investigation of bats-hosts-res..." refers methods in this paper
...The used data for system (1) are for Wuhan, China, [17, 19]....
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...The first wave of outbreak happened in Wuhan, China, and then quickly spread into some other parts of China and even to other countries due to its high person-to-person infection rate....
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TL;DR: A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations and it is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R 0>1,Then it is unstable.
Abstract: A precise definition of the basic reproduction number, Ro, is presented for a general compartmental disease transmission model based on a system of ordinary dierential equations. It is shown that, if Ro 1, then it is unstable. Thus,Ro is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for Ro near one. This criterion, together with the definition of Ro, is illustrated by treatment, multigroup, staged progression, multistrain and vectorhost models and can be applied to more complex models. The results are significant for disease control.
7,106 citations
"New investigation of bats-hosts-res..." refers background in this paper
...When r0 > 1, the outbreak will occur [18], and it is not stable....
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...If r0 < 1, then system (1) is locally asymptotically stable [10, 18], and the outbreak will fade away [18]....
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TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Abstract: In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method.
2,371 citations
TL;DR: It is found that border restrictions and/or internal travel restrictions are unlikely to delay spread by more than 2–3 weeks unless more than 99% effective, and vaccine stockpiled in advance of a pandemic could significantly reduce attack rates even if of low efficacy.
Abstract: Development of strategies for mitigating the severity of a new influenza pandemic is now a top global public health priority. Influenza prevention and containment strategies can be considered under the broad categories of antiviral, vaccine and non-pharmaceutical (case isolation, household quarantine, school or workplace closure, restrictions on travel) measures. Mathematical models are powerful tools for exploring this complex landscape of intervention strategies and quantifying the potential costs and benefits of different options. Here we use a large-scale epidemic simulation to examine intervention options should initial containment of a novel influenza outbreak fail, using Great Britain and the United States as examples. We find that border restrictions and/or internal travel restrictions are unlikely to delay spread by more than 2-3 weeks unless more than 99% effective. School closure during the peak of a pandemic can reduce peak attack rates by up to 40%, but has little impact on overall attack rates, whereas case isolation or household quarantine could have a significant impact, if feasible. Treatment of clinical cases can reduce transmission, but only if antivirals are given within a day of symptoms starting. Given enough drugs for 50% of the population, household-based prophylaxis coupled with reactive school closure could reduce clinical attack rates by 40-50%. More widespread prophylaxis would be even more logistically challenging but might reduce attack rates by over 75%. Vaccine stockpiled in advance of a pandemic could significantly reduce attack rates even if of low efficacy. Estimates of policy effectiveness will change if the characteristics of a future pandemic strain differ substantially from those seen in past pandemics.
2,099 citations
TL;DR: In this article, a variational iteration method is used to give approximate solutions of the problem of seepage flow in porous media with fractional derivatives, and the results show that the proposed iteration method, requiring no linearization or small perturbation is very effective and convenient.
1,265 citations