Chaos, solitons, and fractals最新文献

{"title":"Dynamics of epidemics: Impact of easing restrictions and control of infection spread.","authors":"Silvio L T de Souza,&nbsp;Antonio M Batista,&nbsp;Iberê L Caldas,&nbsp;Kelly C Iarosz,&nbsp;José D Szezech","doi":"10.1016/j.chaos.2020.110431","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110431","url":null,"abstract":"<p><p>During an infectious disease outbreak, mathematical models and computational simulations are essential tools to characterize the epidemic dynamics and aid in design public health policies. Using these tools, we provide an overview of the possible scenarios for the COVID-19 pandemic in the phase of easing restrictions used to reopen the economy and society. To investigate the dynamics of this outbreak, we consider a deterministic compartmental model (SEIR model) with an additional parameter to simulate the restrictions. In general, as a consequence of easing restrictions, we obtain scenarios characterized by high spikes of infections indicating significant acceleration of the spreading disease. Finally, we show how such undesirable scenarios could be avoided by a control strategy of successive partial easing restrictions, namely, we tailor a successive sequence of the additional parameter to prevent spikes in phases of low rate of transmissibility.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110431"},"PeriodicalIF":7.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110431","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38705403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and forecasting the COVID-19 pandemic in India.","authors":"Kankan Sarkar,&nbsp;Subhas Khajanchi,&nbsp;Juan J Nieto","doi":"10.1016/j.chaos.2020.110049","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110049","url":null,"abstract":"<p><p>In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (<i>I_q</i> ) and quarantined susceptible (<i>S_q</i> ), collectively expressed <i>SARII_qS_q</i> . A sensitivity analysis is conducted to determine the robustness of model predictions to parameter values and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in India. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by quarantined the susceptible individuals, can effectively reduce the basic reproduction number. Our model simulations demonstrate that the elimination of ongoing SARS-CoV-2 pandemic is possible by combining the restrictive social distancing and contact tracing. Our predictions are based on real data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110049"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38301395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling, analysis and numerical simulation of the <i>COVID-19</i> transmission with mitigation of control strategies used in Cameroon.","authors":"Seraphin Djaoue,&nbsp;Gabriel Guilsou Kolaye,&nbsp;Hamadjam Abboubakar,&nbsp;Ado Adamou Abba Ari,&nbsp;Irepran Damakoa","doi":"10.1016/j.chaos.2020.110281","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110281","url":null,"abstract":"<p><p>In this paper, we formulated a general model of <i>COVID-19</i>model transmission using biological features of the disease and control strategies based on the isolation of exposed people, confinement (lock-downs) of the human population, testing people living risks area, wearing of masks and respect of hygienic rules. We provide a theoretical study of the model. We derive the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> which determines the extinction and the persistence of the infection. It is shown that the model exhibits a backward bifurcation at <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> . The sensitivity analysis of the model has been performed to determine the impact of related parameters on outbreak severity. It is observed that the asymptomatic infectious group of individuals may play a major role in the spreading of transmission. Moreover, various mitigation strategies are investigated using the proposed model. A numerical evaluation of control strategies has been performed. We found that isolation has a real impact on <i>COVID-19</i> transmission. When efforts are made through the tracing to isolate 80% of exposed people the disease disappears about 100 days. Although partial confinement does not eradicate the disease it is observed that, during partial confinement, when at least 10% of the partially confined population is totally confined, <i>COVID-19</i> spread stops after 150 days. The strategy of massif testing has also a real impact on the disease. In that model, we found that when more than 95% of moderate and symptomatic infected people are identified and isolated, the disease is also really controlled after 90 days. The wearing of masks and respecting hygiene rules are fundamental conditions to control the <i>COVID-19</i>.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110281"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110281","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38424742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An analysis of COVID-19 spread based on fractal interpolation and fractal dimension.","authors":"Cristina-Maria Păcurar,&nbsp;Bogdan-Radu Necula","doi":"10.1016/j.chaos.2020.110073","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110073","url":null,"abstract":"<p><p>The present paper proposes a reconstruction of the epidemic curves from the fractal interpolation point of view. Looking at the epidemic curves as fractal structures might be an efficient way to retrieve missing pieces of information due to insufficient testing and predict the evolution of the disease. A fractal approach of the epidemic curve can contribute to the assessment and modeling of other epidemics. On the other hand, we have considered the spread of the epidemic in countries like Romania, Italy, Spain, and Germany and analyzed the spread of the disease in those countries based on their fractal dimension.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110073"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110073","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38297701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics.","authors":"Peipei Wang,&nbsp;Xinqi Zheng,&nbsp;Jiayang Li,&nbsp;Bangren Zhu","doi":"10.1016/j.chaos.2020.110058","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110058","url":null,"abstract":"<p><p>COVID-19 has now had a huge impact in the world, and more than 8 million people in more than 100 countries are infected. To contain its spread, a number of countries published control measures. However, it's not known when the epidemic will end in global and various countries. Predicting the trend of COVID-19 is an extremely important challenge. We integrate the most updated COVID-19 epidemiological data before June 16, 2020 into the Logistic model to fit the cap of epidemic trend, and then feed the cap value into FbProphet model, a machine learning based time series prediction model to derive the epidemic curve and predict the trend of the epidemic. Three significant points are summarized from our modeling results for global, Brazil, Russia, India, Peru and Indonesia. Under mathematical estimation, the global outbreak will peak in late October, with an estimated 14.12 million people infected cumulatively.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110058"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38297695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel mathematical approach of COVID-19 with non-singular fractional derivative.","authors":"Sachin Kumar,&nbsp;Jinde Cao,&nbsp;Mahmoud Abdel-Aty","doi":"10.1016/j.chaos.2020.110048","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110048","url":null,"abstract":"<p><p>We analyze a proposition which considers new mathematical model of COVID-19 based on fractional ordinary differential equation. A non-singular fractional derivative with Mittag-Leffler kernel has been used and the numerical approximation formula of fractional derivative of function <math> <msup><mrow><mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>a</mi> <mo>)</mo></mrow> <mi>n</mi></msup> </math> is obtained. A new operational matrix of fractional differentiation on domain [0, <i>a</i>], <i>a</i> ≥ 1, <i>a</i> ∈ <i>N</i> by using the extended Legendre polynomial on larger domain has been developed. It is shown that the new mathematical model of COVID-19 can be solved using Legendre collocation method. Also, the accuracy and validity of our developed operational matrix have been tested. Finally, we provide numerical evidence and theoretical arguments that our new model can estimate the output of the exposed, infected and asymptotic carrier with higher fidelity than the previous models, thereby motivating the use of the presented model as a standard tool for examining the effect of contact rate and transmissibility multiple on number of infected cases are depicted with graphs.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110048"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110048","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38301394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Momentum managing epidemic spread and Bessel functions.","authors":"Ivan Cherednik","doi":"10.1016/j.chaos.2020.110234","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110234","url":null,"abstract":"<p><p>Starting with the power law for the total number of detected infections, we propose differential equations describing the effect of momentum epidemic management. Our 2-phase formula matches very well the curves of the total numbers of the Covid-19 infection in many countries; the first phase is described by Bessel functions. It provides projections for the saturation, assuming that the management is steady. We discuss Austria, Brazil, Germany, Japan, India, Israel, Italy, the Netherlands, Sweden, Switzerland, UK, and the USA, including some analysis of the second waves.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110234"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110234","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25314980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study.","authors":"Saif Ullah,&nbsp;Muhammad Altaf Khan","doi":"10.1016/j.chaos.2020.110075","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110075","url":null,"abstract":"<p><p>Coronavirus disease (COVID-19) is the biggest public health challenge the world is facing in recent days. Since there is no effective vaccine and treatment for this virus, therefore, the only way to mitigate this infection is the implementation of non-pharmaceutical interventions such as social-distancing, community lockdown, quarantine, hospitalization or self-isolation and contact-tracing. In this paper, we develop a mathematical model to explore the transmission dynamics and possible control of the COVID-19 pandemic in Pakistan, one of the Asian countries with a high burden of disease with more than 200,000 confirmed infected cases so far. Initially, a mathematical model without optimal control is formulated and some of the basic necessary analysis of the model, including stability results of the disease-free equilibrium is presented. It is found that the model is stable around the disease-free equilibrium both locally and globally when the basic reproduction number is less than unity. Despite the basic analysis of the model, we further consider the confirmed infected COVID-19 cases documented in Pakistan from March 1, till May 28, 2020 and estimate the model parameters using the least square fitting tools from statistics and probability theory. The results show that the model output is in good agreement with the reported COVID-19 infected cases. The approximate value of the basic reproductive number based on the estimated parameters is <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>≈</mo> <mn>1.87</mn></mrow> </math> . The effect of low (or mild), moderate, and comparatively strict control interventions like social-distancing, quarantine rate, (or contact-tracing of suspected people) and hospitalization (or self-isolation) of testing positive COVID-19 cases are shown graphically. It is observed that the most effective strategy to minimize the disease burden is the implementation of maintaining a strict social-distancing and contact-tracing to quarantine the exposed people. Furthermore, we carried out the global sensitivity analysis of the most crucial parameter known as the basic reproduction number using the Latin Hypercube Sampling (LHS) and the partial rank correlation coefficient (PRCC) techniques. The proposed model is then reformulated by adding the time-dependent control variables <i>u</i> ₁(<i>t</i>) for quarantine and <i>u</i> ₂(<i>t</i>) for the hospitalization interventions and present the necessary optimality conditions using the optimal control theory and Pontryagin's maximum principle. Finally, the impact of constant and optimal control interventions on infected individuals is compared graphically.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110075"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38295676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19.","authors":"Chaeyoung Lee,&nbsp;Yibao Li,&nbsp;Junseok Kim","doi":"10.1016/j.chaos.2020.110090","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110090","url":null,"abstract":"<p><p>In this article, we propose the Susceptible-Unidentified infected-Confirmed (SUC) epidemic model for estimating the unidentified infected population for coronavirus disease 2019 (COVID-19) in China. The unidentified infected population means the infected but not identified people. They are not yet hospitalized and still can spread the disease to the susceptible. To estimate the unidentified infected population, we find the optimal model parameters which best fit the confirmed case data in the least-squares sense. Here, we use the time series data of the confirmed cases in China reported by World Health Organization. In addition, we perform the practical identifiability analysis of the proposed model using the Monte Carlo simulation. The proposed model is simple but potentially useful in estimating the unidentified infected population to monitor the effectiveness of interventions and to prepare the quantity of protective masks or COVID-19 diagnostic kit to supply, hospital beds, medical staffs, and so on. Therefore, to control the spread of the infectious disease, it is essential to estimate the number of the unidentified infected population. The proposed SUC model can be used as a basic building block mathematical equation for estimating unidentified infected population.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110090"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38295682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Forecasting COVID-19 pandemic: A data-driven analysis.","authors":"Khondoker Nazmoon Nabi","doi":"10.1016/j.chaos.2020.110046","DOIUrl":"https://doi.org/10.1016/j.chaos.2020.110046","url":null,"abstract":"<p><p>In this paper, a new Susceptible-Exposed-Symptomatic Infectious-Asymptomatic Infectious-Quarantined-Hospitalized-Recovered-Dead (<i>SEI_DI_UQHRD</i>) deterministic compartmental model has been proposed and calibrated for interpreting the transmission dynamics of the novel coronavirus disease (COVID-19). The purpose of this study is to give tentative predictions of the epidemic peak for Russia, Brazil, India and Bangladesh which could become the next COVID-19 hotspots in no time by using a newly developed algorithm based on well-known Trust-region-reflective (TRR) algorithm, which is one of the robust real-time optimization techniques. Based on the publicly available epidemiological data from late January until 10 May, it has been estimated that the number of daily new symptomatic infectious cases for the above mentioned countries could reach the peak around the middle of June with the peak size of  ∼ 15, 774 (95% CI, 12,814-16,734) symptomatic infectious cases in Russia,  ∼ 26, 449 (95% CI, 25,489-31,409) cases in Brazil,  ∼ 9, 504 (95% CI, 8,378-13,630) cases in India and  ∼ 2, 209 (95% CI, 2,078-2,840) cases in Bangladesh if current epidemic trends hold. As of May 11, 2020, incorporating the infectiousness capability of asymptomatic carriers, our analysis estimates the value of the basic reproductive number (<i>R</i> ₀) was found to be  ∼ 4.234 (95% CI, 3.764-4.7) in Russia,  ∼ 5.347 (95% CI, 4.737-5.95) in Brazil,  ∼ 5.218 (95% CI, 4.56-5.81) in India,  ∼ 4.649 (95% CI, 4.17-5.12) in the United Kingdom and  ∼ 3.53 (95% CI, 3.12-3.94) in Bangladesh. Moreover, Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) which is a global sensitivity analysis (GSA) method has been applied to quantify the uncertainty of our model mechanisms, which elucidates that for Russia, the recovery rate of undetected asymptomatic carriers, the rate of getting home-quarantined or self-quarantined and the transition rate from quarantined class to susceptible class are the most influential parameters, whereas the rate of getting home-quarantined or self-quarantined and the inverse of the COVID-19 incubation period are highly sensitive parameters in Brazil, India, Bangladesh and the United Kingdom which could significantly affect the transmission dynamics of the novel coronavirus disease (COVID-19). Our analysis also suggests that relaxing social distancing restrictions too quickly could exacerbate the epidemic outbreak in the above-mentioned countries.</p>","PeriodicalId":520585,"journal":{"name":"Chaos, solitons, and fractals","volume":" ","pages":"110046"},"PeriodicalIF":7.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.chaos.2020.110046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38301424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}