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Register a new userSIR Model-based Prediction of Infected Population of Coronavirus in Hubei Province
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After the sudden outbreak of Coronavirus in Wuhan, continuous and rich data of the epidemic has been made public as the vital fact for decision support in control measures and aggressive implementation of containment strategies and plans. With the further growth and spreading of the virus, future resource allocation and planning under updated strategies and measures rely on careful study of the epidemic data and characteristics for accurate prediction and estimation. By using the SIR model and reported data, key parameters are obtained from least sum of squared errors for an accurate prediction of epidemic trend in the last four weeks.
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At the moment of writing (12 February, 2020), the future evolution of the 2019-nCoV virus is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the 2019-nCoV epidemic in the Hubei province. The network is composed of the cities in Hubei and their interactions (e.g., traffic flow). However, the precise interactions between cities is unknown and must be inferred from observing the epidemic. We propose a network-based method to predict the future prevalence of the 2019-nCoV virus in every city. Our results indicate that network-based modelling is beneficial for an accurate forecast of the epidemic outbreak.
The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any strategy about the preventive measures needs to be based upon detailed analysis of the COVID-19 outbreak and accurate scientific predictions. In this paper, we conduct mathematical and numerical analysis to come up with reliable and accurate predictions of the outbreak in Pakistan. The time-dependent Susceptible-Infected-Recovered (SIR) model is used to fit the data and provide future predictions. The turning point of the peak of the pandemic is defined as the day when the transmission rate becomes less than the recovering rate. We have predicted that the outbreak will reach its maximum peak occurring from late May to 9 June with unrecovered number of Infectives in the range 20000-47000 and the cumulative number of infected cases in the range of 57500-153100. The number of Infectives will remain at the lower end in the lock-down scenario but can rapidly double or triple if the spread of the epidemic is not curtailed and localized. The uncertainty on single day projection in our analysis after April 15 is found to be within 5%.
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two populations of susceptible persons, one which obeys confinement and for which the infection rate does not exceed 1, and a population which, being non confined for various imperatives, can be substantially more infective. The model, initially formulated as a differential system, is discretised following a specific procedure, the discrete system serving as an integrator for the differential one. Our model is calibrated so as to correspond to what is observed in the COVID-19 epidemic. Several conclusions can be reached, despite the very simple structure of our model. First, it is not possible to pinpoint the genesis of the epidemic by just analysing data from when the epidemic is in full swing. It may well turn out that the epidemic has reached a sizeable part of the world months before it became noticeable. Concerning the confinement scenarios, a universal feature of all our simulations is that relaxing the lockdown constraints leads to a rekindling of the epidemic. Thus we sought the conditions for the second epidemic peak to be lower than the first one. This is possible in all the scenarios considered (abrupt, progressive or stepwise exit) but typically a progressive exit can start earlier than an abrupt one. However, by the time the progressive exit is complete, the overall confinement times are not too different. From our results, the most promising strategy is that of a stepwise exit. And in fact its implementation could be quite feasible, with the major part of the population (minus the fragile groups) exiting simultaneously but obeying rigorous distancing constraints.
Objectives.--To estimate the basic reproduction number of the Wuhan novel coronavirus (2019-nCoV). Methods.--Based on the susceptible-exposed-infected-removed (SEIR) compartment model and the assumption that the infectious cases with symptoms occurred before January 25, 2020 are resulted from free propagation without intervention, we estimate the basic reproduction number of 2019-nCoV according to the reported confirmed cases and suspected cases, as well as the theoretical estimated number of infected cases by other research teams, together with some epidemiological determinants learned from the severe acute respiratory syndrome. Results The basic reproduction number falls between 2.8 to 3.3 by using the real-time reports on the number of 2019-nCoV infected cases from Peoples Daily in China, and falls between 3.2 and 3.9 on the basis of the predicted number of infected cases from colleagues. Conclusions.--The early transmission ability of 2019-nCoV is closed to or slightly higher than SARS. It is a controllable disease with moderate-high transmissibility. Timely and effective control measures are needed to suppress the further transmissions. Notes Added.--Using a newly reported epidemiological determinants for early 2019-nCoV, the estimated basic reproduction number is in the range [2.2,3.0].
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the eventual vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number $R_0$ for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated in all the studied models. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces $R_0$ and delays the disease prevalence, and thus is essential to containing epidemics.
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