World Health Organization (WHO) has declared COVID-19 a pandemic on March 11, 2020. As of May 23, 2020, according to WHO, there are 213 countries, areas or territories with COVID-19 positive cases. To effectively address this situation, it is imperative to have a clear understanding of the COVID-19 transmission dynamics and to concoct efficient control measures to mitigate/contain the spread. In this work, the COVID-19 dynamics is modelled using susceptible–exposed–infectious–removed model with a nonlinear incidence rate. In order to control the transmission, the coefficient of nonlinear incidence function is adopted as the Governmental control input. To adequately understand the COVID-19 dynamics, bifurcation analysis is performed and the effect of varying reproduction number on the COVID-19 transmission is studied. The inadequacy of an open-loop approach in controlling the disease spread is validated via numerical simulations and a robust closed-loop control methodology using sliding mode control is also presented. The proposed SMC strategy could bring the basic reproduction number closer to 1 from an initial value of 2.5, thus limiting the exposed and infected individuals to a controllable threshold value. The model and the proposed control strategy are then compared with real-time data in order to verify its efficacy.
相似文献In this paper, a delay-differential mathematical model that described HIV infection of CD4+ T cells is analyzed. The effect of time delay on stability of the equilibria of the infection model has been studied. And the sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the uninfected equilibrium are given. By using the geometric stability switch criterion in the delay-differential system with delay-dependent parameters, we present that stable equilibria become unstable as the time delay increases. Numerical simulations are carried out to explain the mathematical conclusions.
相似文献One of the main concerns during the COVID-19 pandemic was the protection of healthcare workers against the novel coronavirus. The critical role and vulnerability of healthcare workers during the COVID-19 pandemic leads us to derive a mathematical model to express the spread of coronavirus between the healthcare workers. In the first step, the SECIRH model is introduced, and then the mathematical equations are written. The proposed model includes eight state variables, i.e., Susceptible, Exposed, Carrier, Infected, Hospitalized, ICU admitted, Dead, and finally Recovered. In this model, the vaccination, protective equipment, and recruitment policy are considered as preventive actions. The formal confirmed data provided by the Iranian ministry of health is used to simulate the proposed model. The simulation results revealed that the proposed model has a high degree of consistency with the actual COVID-19 daily statistics. In addition, the roles of vaccination, protective equipment, and recruitment policy for the elimination of coronavirus among the healthcare workers are investigated. The results of this research help the policymakers to adopt the best decisions against the spread of coronavirus among healthcare workers.
相似文献SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) has been causing an outbreak of a new type of pneumonia globally, and repeated outbreaks have already appeared. Among the studies on the spread of the COVID-19, few studies have investigated the repeated outbreaks in stages, and the quantitative condition of a controllable spread has not been revealed. In this paper, a brief compartmental model is developed. The effective reproduction number (ERN) of the model is interpreted by the ratio of net newly infectious individuals to net isolation infections to assess the controllability of the spread of COVID-19. It is found that the value of the ERN at the inflection point of the pandemic is equal to one. The effectiveness of the quarantine, even the treatment, is parametrized in various stages with Gompertz functions to increase modeling accuracy. The impacts of the vaccinations are discussed by adding a vaccinated compartment. The results show that the sufficient vaccinations can make the inflection point appear early and significantly reduce subsequent increases in newly confirmed cases. The analysis of the ERNs of COVID-19 in the United States, Spain, France, and Peru confirms that the condition of a repeated outbreak is to relax or lift the interventions related to isolation and quarantine interventions to a level where the ERN is greater than one.
相似文献Since the outbreak of coronavirus disease in 2019 (COVID-19), the disease has rapidly spread to the world, and the cumulative number of cases is now more than 2.3 million. We aim to study the spread mechanism of rumors on social network platform during the spread of COVID-19 and consider education as a control measure of the spread of rumors. Firstly, a novel epidemic-like model is established to characterize the spread of rumor, which depends on the nonautonomous partial differential equation. Furthermore, the registration time of network users is abstracted as ‘age,’ and the spreading principle of rumors is described from two dimensions of age and time. Specifically, the susceptible users are divided into higher-educators class and lower-educators class, in which the higher-educators class will be immune to rumors with a higher probability and the lower-educators class is more likely to accept and spread the rumors. Secondly, the existence and uniqueness of the solution is discussed and the stability of steady-state solution of the model is obtained. Additionally, an interesting conclusion is that the education level of the crowd is an essential factor affecting the final scale of the spread of rumors. Finally, some control strategies are presented to effectively restrain the rumor propagation, and numerical simulations are carried out to verify the main theoretical results.
相似文献34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin’s maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.
相似文献The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.
相似文献We developed an endemic model of COVID-19 to assess the impact of vaccination and immunity waning on the dynamics of the disease. Our model exhibits the phenomenon of backward bifurcation and bi-stability, where a stable disease-free equilibrium coexists with a stable endemic equilibrium. The epidemiological implication of this is that the control reproduction number being less than unity is no longer sufficient to guarantee disease eradication. We showed that this phenomenon could be eliminated by either increasing the vaccine efficacy or by reducing the disease transmission rate (adhering to non-pharmaceutical interventions). Furthermore, we numerically investigated the impacts of vaccination and waning of both vaccine-induced immunity and post-recovery immunity on the disease dynamics. Our simulation results show that the waning of vaccine-induced immunity has more effect on the disease dynamics relative to post-recovery immunity waning and suggests that more emphasis should be on reducing the waning of vaccine-induced immunity to eradicate COVID-19.
相似文献We have developed a mathematical model and stochastic numerical simulation for the transmission of COVID-19 and other similar infectious diseases that accounts for the geographic distribution of population density, detailed down to the level of location of individuals, and age-structured contact rates. Our analytical framework includes a surrogate model optimization process to rapidly fit the parameters of the model to the observed epidemic curves for cases, hospitalizations, and deaths. This toolkit (the model, the simulation code, and the optimizer) is a useful tool for policy makers and epidemic response teams, who can use it to forecast epidemic development scenarios in local settings (at the scale of cities to large countries) and design optimal response strategies. The simulation code also enables spatial visualization, where detailed views of epidemic scenarios are displayed directly on maps of population density. The model and simulation also include the vaccination process, which can be tailored to different levels of efficiency and efficacy of different vaccines. We used the developed framework to generate predictions for the spread of COVID-19 in the canton of Geneva, Switzerland, and validated them by comparing the calculated number of cases and recoveries with data from local seroprevalence studies.
相似文献In this paper, we propose a non-smooth Filippov system that describes the interaction of the pest and natural enemy with considering time delay, which represents the change in the growth rate of natural enemies before it is released to prey on pests. When the number of the pest is below the threshold, no control is applied; otherwise, control measures will be adopted. We discuss the stability of the equilibria and the existence of Hopf bifurcation. The results show that the Hopf bifurcation occurs when the time delay passes through some critical values. By applying the Filippov convex method, we obtain the dynamics of the sliding mode. The solutions of the system eventually tend toward the regular equilibrium, the pseudo-equilibrium or a standard periodic solution. Numerical simulations show that time delay plays an important role in local and global sliding bifurcations. We can obtain boundary focus bifurcations from boundary node bifurcations by varying time delay. Furthermore, touching, buckling and crossing bifurcations can be obtained frequently by increasing time delay. The results can provide some insights in pest control.
相似文献The COVID-19 pandemic shows to have a huge impact on people's health and countries' infrastructures around the globe. Iran was one of the first countries that experienced the vast prevalence of the coronavirus outbreak. The Iranian authorities applied various non-pharmaceutical interventions to eradicate the epidemic in different periods. This study aims to investigate the effectiveness of non-pharmaceutical interventions in managing the current Coronavirus pandemic and to predict the next wave of infection in Iran. To achieve the research objective, the number of cases and deaths before and after the interventions was studied and the effective reproduction number of the infection was analyzed under various scenarios. The SEIR generic model was applied to capture the dynamic of the pandemic in Iran. To capture the effects of different interventions, the corresponding reproduction number was considered. Depending on how people are responsive to interventions, the effectiveness of each intervention has been investigated. Results show that the maximum number of the total of infected individuals will occur around the end of May and the start of June 2021. It is concluded that the outbreak could be smoothed if full lockdown and strict quarantine continue. The proposed modeling could be used as an assessment tool to evaluate the effects of different interventions in new outbreaks.
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