scholarly journals Epidemic Models with Random Infectious Period

2020 ◽  
Author(s):  
Germán Riaño
Keyword(s):  
Public Policy ◽  
Exponential Distribution ◽  
Numerical Experiments ◽  
Sir Model ◽  
Transmission Model ◽  
General Distribution ◽  
Infectious Period ◽  
Basic Model ◽  
Sir Epidemic ◽  
Lower Variability

In this paper, we present an extension to the classical SIR epidemic transmission model that uses any general probability distribution for the length of the infectious period. The classical SIR model implicitly requires an exponential distribution for the length of this period of time. We will show how a general distribution can be easily taken into account using the Transient Little Law and present numerical methods to solve the model in an efficient way. Our numerical experiments show that in the presence of a more realistic distribution, with lower variability than the exponential distribution, the size of peak of infected individuals on the graph will be higher and occur earlier. Conversely, a higher-variability distribution will lead to a lower peak that takes longer to dissipate. We also discuss some extensions to the basic model, to include variants like SEIRD and SIS. These findings should have profound and important consequences in the design of public policy.

A stochastic SIR model for analysis of testosterone suppression of CRH-stimulated cortisol in men

2021 ◽  
Author(s):  
A. Manickam ◽  
Pushpendra Kumar ◽  
K. Dasunaidu ◽  
V. Govindaraj ◽  
Dheeraj Kumar Joshi
Keyword(s):  
Mathematical Model ◽  
Medical Research ◽  
Hpa Axis ◽  
Sir Model ◽  
Transmission Model ◽  
Medical Field ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Given

A stochastic SIR influenza vertical transmission model is examined in this paper where vaccination and an incidence rate that is not linear are considered. To determine whether testosterone regulates lower sintering HPA axis function in males, we used a stochastic SIR epidemic procedure with divergent influences on ACTH and cortisol. The suppressive effects on cortisol can be attributed to a peripheral (adrenal) locus. Following that, we came to the conclusion that experimental solutions have been discovered and the requisite statistical findings have been examined. Finally, we deduce that the given mathematical model and the results are relevant to medical research. In the future, this research can be further extended to simulate more results in the medical field.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

scholarly journals Establishment, contagiousness, and initial spread of SARS-CoV-2 in Canada

FACETS ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 180-194
Author(s):  
Martin Krkošek ◽  
Madeline Jarvis-Cross ◽  
Kiran Wadhawan ◽  
Isha Berry ◽  
Jean-Paul R. Soucy ◽  
...  
Keyword(s):  
Latent Period ◽  
Bayesian Framework ◽  
Contact Tracing ◽  
Transmission Model ◽  
Infectious Period ◽  
Median Reduction ◽  
Community Transmission

This study empirically quantifies dynamics of SARS-CoV-2 establishment and early spread in Canada. We developed a transmission model that was simulation tested and fitted in a Bayesian framework to timeseries of new cases per day prior to physical distancing interventions. A hierarchical version was fitted to all provinces simultaneously to obtain average estimates for Canada. Across scenarios of a latent period of 2–4 d and an infectious period of 5–9 d, the R0 estimate for Canada ranges from a minimum of 3.0 (95% CI: 2.3–3.9) to a maximum of 5.3 (95% CI: 3.9–7.1). Among provinces, the estimated commencement of community transmission ranged from 3 d before to 50 d after the first reported case and from 2 to 25 d before the first reports of community transmission. Among parameter scenarios and provinces, the median reduction in transmission needed to obtain R0 < 1 ranged from 46% (95% CI: 43%–48%) to 89% (95% CI: 88%–90%). Our results indicate that local epidemics of SARS-CoV-2 in Canada entail high levels of stochasticity, contagiousness, and observation delay, which facilitates rapid undetected spread and requires comprehensive testing and contact tracing for its containment.

scholarly journals Stiffness Analysis to Predict the Spread Out of Fake Information

2021 ◽  
Vol 13 (9) ◽  
pp. 222
Author(s):  
Raffaele D'Ambrosio ◽  
Giuseppe Giordano ◽  
Serena Mottola ◽  
Beatrice Paternoster
Keyword(s):  
Numerical Experiments ◽  
Real Data ◽  
Sir Model ◽  
Stiffness Index ◽  
Fake News ◽  
Stiffness Analysis ◽  
Data Support

This work highlights how the stiffness index, which is often used as a measure of stiffness for differential problems, can be employed to model the spread of fake news. In particular, we show that the higher the stiffness index is, the more rapid the transit of fake news in a given population. The illustration of our idea is presented through the stiffness analysis of the classical SIR model, commonly used to model the spread of epidemics in a given population. Numerical experiments, performed on real data, support the effectiveness of the approach.

scholarly journals The attainment of herd immunity with a reducing risk of contact infection in modelling 

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M Peariasamy ◽  
Hishamshah Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Model ◽  
Force Of Infection ◽  
Initial Stage ◽  
And Control ◽  
Model Features

Abstract The risk of contact infection among susceptible individuals in a randomly mixed population can be reduced by the presence of immune individuals and this principle forms the fundamental of herd immunity. The conventional susceptible-infectious-recovered (SIR) model features an infection-induced herd immunity model, but does not include the reducing risk of contact infection among susceptible individuals in the transmission model, therefore tends to overestimate the transmission dynamics of infectious diseases. Here we show that the reducing risk of contact infection among susceptible individuals can be achieved by incorporating the proportion of susceptible individuals (model A) or the inverse of proportion of recovered individuals (model B) in the force of infection of the SIR model. We numerically simulated the conventional SIR model and both new SIR models A and B under the exact condition with a basic reproduction number of 3·0. Prior to the numerical simulation, the threshold for the eradication of infectious disease through herd immunity was expected to be 0·667 (66·7%) for all three models. All three models performed likewise at the initial stage of disease transmission. In the conventional SIR model, the infectious disease subsided when 94·0 % of the population had been infected and recovered, way above the expected threshold for eradication and control of the infectious disease. Both models A and B simulated the infectious disease to diminish when 66·7% and 75·6% of the population had been infected, showing herd immunity might protect more susceptible individuals from the infectious disease as compared to the projection generated by the conventional SIR. Our study shows that model A provides a better framework for modelling herd immunity through vaccination, while model B provides a better framework for modelling herd immunity through infection. Both models overcome the insufficiency of the conventional SIR model in attaining the effect of herd immunity in modelling outputs, which is important and relevant for modelling infectious disease, such as the COVID-19 in a randomly mixed population.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

EXACT ANALYTICAL EXPRESSIONS FOR THE FINAL EPIDEMIC SIZE OF AN SIR MODEL ON SMALL NETWORKS

2016 ◽  
Vol 57 (4) ◽  
pp. 429-444 ◽  
Author(s):  
K. MCCULLOCH ◽  
M. G. ROBERTS ◽  
C. R. LAING
Keyword(s):  
Initial Conditions ◽  
Transmission Rate ◽  
Sir Model ◽  
Contact Network ◽  
Sir Epidemic Model ◽  
Node Number ◽  
Sir Epidemic ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
Analytical Expressions

We investigate the dynamics of a susceptible infected recovered (SIR) epidemic model on small networks with different topologies, as a stepping stone to determining how the structure of a contact network impacts the transmission of infection through a population. For an SIR model on a network of$N$nodes, there are$3^{N}$configurations that the network can be in. To simplify the analysis, we group the states together based on the number of nodes in each infection state and the symmetries of the network. We derive analytical expressions for the final epidemic size of an SIR model on small networks composed of three or four nodes with different topological structures. Differential equations which describe the transition of the network between states are also derived and solved numerically to confirm our analysis. A stochastic SIR model is numerically simulated on each of the small networks with the same initial conditions and infection parameters to confirm our results independently. We show that the structure of the network, degree of the initial infectious node, number of initial infectious nodes and the transmission rate all significantly impact the final epidemic size of an SIR model on small networks.

scholarly journals Modelling song popularity as a contagious process

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210457
Author(s):  
Dora P. Rosati ◽  
Matthew H. Woolhouse ◽  
Benjamin M. Bolker ◽  
David J. D. Earn
Keyword(s):  
Infectious Disease ◽  
Time Series ◽  
Disease Transmission ◽  
Sir Model ◽  
Sir Epidemic Model ◽  
Infectious Disease Transmission ◽  
Download Time ◽  
Sir Epidemic ◽  
Popular Songs ◽  
Song Preferences

Popular songs are often said to be ‘contagious’, ‘infectious’ or ‘viral’. We find that download count time series for many popular songs resemble infectious disease epidemic curves. This paper suggests infectious disease transmission models could help clarify mechanisms that contribute to the ‘spread’ of song preferences and how these mechanisms underlie song popularity. We analysed data from MixRadio, comprising song downloads through Nokia cell phones in Great Britain from 2007 to 2014. We compared the ability of the standard susceptible–infectious–recovered (SIR) epidemic model and a phenomenological (spline) model to fit download time series of popular songs. We fitted these same models to simulated epidemic time series generated by the SIR model. Song downloads are captured better by the SIR model, to the same extent that actual SIR simulations are fitted better by the SIR model than by splines. This suggests that the social processes underlying song popularity are similar to those that drive infectious disease transmission. We draw conclusions about song popularity within specific genres based on estimated SIR parameters. In particular, we argue that faster spread of preferences for Electronica songs may reflect stronger connectivity of the ‘susceptible community’, compared with the larger and broader community that listens to more common genres.

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