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Register a new userA prognostic dynamic model applicable to infectious diseases providing easily visualized guides -- A case study of COVID-19 in the UK
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Authors
Yuxuan Zhang
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A reasonable prediction of infectious diseases transmission process under different disease control strategies is an important reference point for policy makers. Here we established a dynamic transmission model via Python and realized comprehensive regulation of disease control measures. We classified government interventions into three categories and introduced three parameters as descriptions for the key points in disease control, these being intraregional growth rate, interregional communication rate, and detection rate of infectors. Our simulation predicts the infection by COVID-19 in the UK would be out of control in 73 days without any interventions; at the same time, herd immunity acquisition will begin from the epicentre. After we introduced government interventions, single intervention is effective in disease control but at huge expense while combined interventions would be more efficient, among which, enhancing detection number is crucial in control strategy of COVID-19. In addition, we calculated requirements for the most effective vaccination strategy based on infection number in real situation. Our model was programmed with iterative algorithms, and visualized via cellular automata, it can be applied to similar epidemics in other regions if the basic parameters are inputted, and is able to synthetically mimick the effect of multiple factors in infectious disease control.
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In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called textit{level of abstraction} used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online.
We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al., Comp. Meth. App. Mech. Eng., 356, 44-74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.
An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will end up and by when. South African data for the period from 23 March to 8 May 2020 is then used to obtain SEIQRDP model parameters. It is found that the model fits the initial disease progression well, but that the long-term predictive capability of the model is rather poor. The South African SEIQRDP model is subsequently recalculated with the basic reproduction number constrained to reported values. The resulting model fits the data well, and long-term predictions appear to be reasonable. The South African SEIQRDP model predicts that the peak in the number of confirmed infectious individuals will occur at the end of October 2020, and that the total number of deaths will range from about 10,000 to 90,000, with a nominal value of about 22,000. All of these predictions are heavily dependent on the disease control measures in place, and the adherence to these measures. These predictions are further shown to be particularly sensitive to parameters used to determine the basic reproduction number. The future aim is to use a feedback control approach together with the South African SEIQRDP model to determine the epidemiological impact of varying lockdown levels proposed by the South African Government.
We consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This SHIR model is applied to COVID-19 data, and shows promise as a simple, tractable formalism with few parameters that can be used to model pandemic case numbers. As an example we show that the average time dependence of new COVID-19 cases per day from 15 Central and Western European countries is in good agreement with the analytic, parameter-free prediction of the model
Understanding dynamics of an outbreak like that of COVID-19 is important in designing effective control measures. This study aims to develop an agent based model that compares changes in infection progression by manipulating different parameters in a synthetic population. Model input includes population characteristics like age, sex, working status etc. of each individual and other factors influencing disease dynamics. Depending on number of epicentres of infection, location of primary cases, sensitivity, proportion of asymptomatic and frequency or duration of lockdown, our simulator tracks every individual and hence infection progression through community over time. In a closed community of 10000 people, it is seen that without any lockdown, number of cases peak around 6th week and wanes off around 15th week. If primary case is located inside dense population cluster like slums, cases peak early and wane off slowly. With introduction of lockdown, cases peak at slower rate. If sensitivity of identifying infection decreases, cases and deaths increase. Number of cases declines with increase in proportion of asymptomatic cases. The model is robust and provides reproducible estimates with realistic parameter values. It also guides in identifying measures to control outbreak in a community. It is flexible in accommodating different parameters like infectivity period, yield of testing, socio-economic strata, daily travel, awareness level, population density, social distancing, lockdown etc. and can be tailored to study other infections with similar transmission pattern.
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