At present, more and more countries have entered the parallel stage of fighting the epidemic and restoring the economy after reaching the inflection point. Due to economic pressure, the government of India had to implement a policy of relaxing control during the rising period of the epidemic. This paper proposes a compartment model to study the development of COVID-19 in India after relaxing control. The Sigmoid function reflecting the cumulative effect is used to characterize the model-based diagnosis rate, cure rate and mortality rate. Considering the influence of the lockdown on the model parameters, the data are fitted using the method of least squares before and after the lockdown. According to numerical simulation and model analysis, the impact of India’s relaxation of control before and after the inflection point is studied. Research shows that adopting a relaxation policy prematurely will have disastrous consequences. Even if the degree of relaxation is only 5% before the inflection point, it will increase the number of deaths by 15.03%. If the control is relaxed after the inflection point, the higher degree of relaxation, the more likely a secondary outbreak will occur, which will extend the duration of the pandemic, leading to more deaths and put more pressure on the health care system. It is found that after the implementation of the relaxation policy, medical quarantine capability and public cooperation are two vital indicators. The results show that if the supply of kits and detection speed can be increased after the control is relaxed, the secondary outbreak can be effectively avoided. Meanwhile, the increase in public cooperation can significantly reduce the spread of the virus, suppress the second outbreak of the pandemic and reduce the death toll. It is of reference significance to the government’s policy formulation.
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.
相似文献In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.
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In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible–infected–removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.
相似文献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We present results on the mortality statistics of the COVID-19 epidemic in a number of countries. Our data analysis suggests classifying countries in five groups, (1) Western countries, (2) East Block, (3) developed Southeast Asian countries, (4) Northern Hemisphere developing countries and (5) Southern Hemisphere countries. Comparing the number of deaths per million inhabitants, a pattern emerges in which the Western countries exhibit the largest mortality rate. Furthermore, comparing the running cumulative death tolls as the same level of outbreak progress in different countries reveals several subgroups within the Western countries and further emphasises the difference between the five groups. Analysing the relationship between deaths per million and life expectancy in different countries, taken as a proxy of the preponderance of elderly people in the population, a main reason behind the relatively more severe COVID-19 epidemic in the Western countries is found to be their larger population of elderly people, with exceptions such as Norway and Japan, for which other factors seem to dominate. Our comparison between countries at the same level of outbreak progress allows us to identify and quantify a measure of efficiency of the level of stringency of confinement measures. We find that increasing the stringency from 20 to 60 decreases the death count by about 50 lives per million in a time window of 20 days. Finally, we perform logistic equation analyses of deaths as a means of tracking the dynamics of outbreaks in the “first wave” and estimating the associated ultimate mortality, using four different models to identify model error and robustness of results. This quantitative analysis allows us to assess the outbreak progress in different countries, differentiating between those that are at a quite advanced stage and close to the end of the epidemic from those that are still in the middle of it. This raises many questions in terms of organisation, preparedness, governance structure and so on.
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In view of the facts in the infection and propagation of COVID-19, a stochastic reaction–diffusion epidemic model is presented to analyse and control this infectious diseases. Stationary distribution and Turing instability of this model are discussed for deriving the sufficient criteria for the persistence and extinction of disease. Furthermore, the amplitude equations are derived by using Taylor series expansion and weakly nonlinear analysis, and selection of Turing patterns for this model can be determined. In addition, the optimal quarantine control problem for reducing control cost is studied, and the differences between the two models are compared. By applying the optimal control theory, the existence and uniqueness of the optimal control and the optimal solution are obtained. Finally, these results are verified and illustrated by numerical simulation.
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