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Sources of data/modeling
Published in Edward M. Rafalski, Ross M. Mullner, Healthcare Analytics, 2022
Edward M. Rafalski, Robert Marksthaler
An SIR model is an epidemiological model that computes the theoretical number of people infected with a contagious illness in a closed population over time. As explained earlier, the name of this class of models derives from the fact that they involve coupled equations relating the number of susceptible people S(t), number of people infected I(t), and number of people who have recovered R(t). One of the simplest SIR models is the Kermack-McKendrick model, originally developed in the wake of numerous plague and cholera epidemics in London.5 As local COVID data became available, incidence, which is a measure of the proportion of new cases per time period, became a useful variable to predict hospital admission using proportion assumptions. For example, based on acuity, a certain proportion of new cases would require admission and the exact opposite proportion would not. Additionally, as testing became more readily available and accessible, positive testing and the infection rates in the general population also became useful variables against which to project trends. This was especially useful for health systems that were operating their own testing sites. Prevalence, which is reflective of the proportion of persons who have a condition at or during a particular time period, was less useful in modeling because it was not sensitive enough to predict surges in new cases which were the primary concern of hospital modeling teams.
Biological Examples Modeled by Discrete Markov Chains
Published in Lyle D. Broemeling, Bayesian Analysis of Infectious Diseases, 2021
The SIR model is an abbreviation for susceptible people, infected, and removed individuals during the course of an epidemic. A person is susceptible if they have not had the disease infected if currently have the disease, and removed if they have had the disease and have since recovered (and are now immune) or have died. Time is measured in discrete steps and at each step each individual can infect susceptible individuals or can recover/die, at which point the infected is removed. Therefore, this version of an epidemic is more realistic than the previous model. Suppose S(t), I(t), and R(t) denote the number of susceptible individuals, infected, and removed at time t, where at each time point each infected has a probability α of infecting each susceptible (this assumes each person has an equal chance of contacting all susceptible persons). At the end of each step, after having had a chance to infect people, each infected person has probability β of being removed. The initial conditions are S(0) = N, I(0) = 1, R(0) = 0, where the total population is of size N + 1 and remains fixed (is not random), that is, S(t) + I(t) + R(t) = N + 1, for all t = 0,1,2,…
The Ecology of Parasitism
Published in Eric S. Loker, Bruce V. Hofkin, Parasitology, 2015
Eric S. Loker, Bruce V. Hofkin
Because it is difficult, if not impossible, to enumerate the actual number of individual microparasites (viruses, bacteria, or protozoans) inhabiting the body of an infected individual, a common approach for modeling microparasite infections has been to use the individual host as the basic unit of study. One basic approach (Figure 6.34) is to divide the host population into three categories: susceptible (S), infected (I), and recovered (R), the SIR model first developed in depth by Kermack and McKendrick and later expanded and popularized in treatments by Anderson and May and by Keeling and Rohani.
Bayesian compartmental model for an infectious disease with dynamic states of infection
Published in Journal of Applied Statistics, 2019
Marie V. Ozanne, Grant D. Brown, Jacob J. Oleson, Iraci D. Lima, Jose W. Queiroz, Selma M. B. Jeronimo, Christine A. Petersen, Mary E. Wilson
Multinomial logistic regression has two implementation advantages over the compartmental modeling approach. First, there are several R packages that implement the model, both in the frequentist and Bayesian frameworks. Second, the model runs quickly for reasonably small sample sizes. For our simulation study, for example, there were a total of 2800 observations (100 observations at each of 28 time points). The multinomial logistic regression model took 43.46 seconds to run for 100,000 iterations using the MCMCmnl function from the MCMCpack package [26]. In contrast, the compartmental model took 919.19 seconds to run under the same conditions. The code for the compartmental model was written by the authors and is available in the supplementary materials, but it has not yet been optimized. Since the code for the compartmental model has not been fully optimized yet, it may be possible to fit the model more efficiently. While some readers may be concerned about the computation time needed to fit the SIR model, the time required is still neglible relative to the length of study. It should be noted that the R package pomp can be used to fit compartmental epidemiological models as well.
Estimation of the doubling time and reproduction number for COVID-19
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Shamim Ahmed, Mohammad Shemanto, Hasin Azhari, Golam Zakaria
The SIR model is an epidemiological model that can compute the number of people infected with a contagious disease over time. The origin of such model is from the work of Kermack and McKendrick (1927). The total population in this model is divided into three categories viz. susceptible, infected, and recovered. Some assumptions are made. The population is considered closed. No one is added to the susceptible group, ignoring births and immigration. The only way an individual leaves the susceptible group is by becoming infected. Furthermore, we assume a homogeneous mixing of the population. The constant transmission rate and removal rate had been assumed. The function of SIR model is illustrated in Figure 1.
A multi-stage SEIR(D) model of the COVID-19 epidemic in Korea
Published in Annals of Medicine, 2021
The original SIR model assumes that (1) the susceptible population is relatively homogeneous, and that (2) parameters used in the model remain invariant throughout the entire epidemic period. In the real-world, however, the susceptible population is not homogeneous. Nor is it that the one-time transmission dynamics captured by the estimated model parameters stay constant throughout the whole period of observation. More importantly, the public health authority’s non-pharmaceutical interventions (NPIs), even in the absence of vaccines and medical treatments, can significantly alter the value of parameters, drastically changing the transmission dynamics of the COVID-19 epidemic. [6,7]