Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period

2021 ◽  
Vol 566 ◽  
pp. 125606
Author(s):  
Daisuke Satoh ◽  
Masato Uchida
Keyword(s):  
Riccati Equation ◽  
Sir Model ◽  
Infectious Period ◽  
Computer Worms ◽  
Discrete Sir Model

A Modified Discrete SIR Model

2003 ◽  
Vol 34 (5) ◽  
pp. 399 ◽  
Author(s):  
Jennifer Switkes
Keyword(s):  
Sir Model ◽  
Discrete Sir Model

scholarly journals Observing the epidemiological SIR model on COVID-19 pandemic data

2021 ◽  
Vol 18 (1) ◽  
pp. 35
Author(s):  
Sergio Rojas
Keyword(s):  
Numerical Solutions ◽  
Disease Model ◽  
Vertical Motion ◽  
Undergraduate Curriculum ◽  
Sir Model ◽  
Infectious Period ◽  
Data Set ◽  
Physics Courses ◽  
Type Differential Equation ◽  
Introductory Physics Courses

This article shows that in the period January 22-June 04, 2020, the combined  data set of cumulative  recoveries and deaths from the current coronavirus COVID-19 pandemic falls on the Kermack and McKendrick approximated solution of the epidemiological {\sir} contagious disease model. Then, as an original contribution of this work, based on the knowledge of the infectious period of any epidemic, a methodology is presented that helps to find numerical solutions of the full {\sir} model that falls on the observed data of the epidemic in case it could be described by the {\sir} model. The methodology is first illustrated by finding a solution of the {\sir} model that falls on the epidemic data of the Bombay plague of 1905-06 analyzed by Kermack and McKendrick. After that, the methodology is applied on analyzing the previously considered coronavirus COVID-19 pandemic data set. Moreover,  since the Kermack and McKendrick approximated solution of the {\sir} model comes from solving a Riccati type differential equation, commonly found when studying (in introductory physics courses) the vertical motion of objects on a resistive medium, enough details are given in the article so the epidemiological {\sir} model can be used as an additional example for enhancing and enriching the undergraduate curriculum Physics courses for Biology, Life Sciences, Medicine and/or Computational Modeling.

scholarly journals The SIR model towards the data

2021 ◽  
Vol 136 (8) ◽  
Author(s):  
Ignazio Lazzizzera
Keyword(s):  
Generation Time ◽  
Reproduction Number ◽  
Removal Rate ◽  
Sir Model ◽  
Infectious Period ◽  
Third Wave ◽  
Real Numbers ◽  
The Third ◽  
Study Case ◽  
Good Agreement

AbstractIn this work, the SIR epidemiological model is reformulated so to highlight the important effective reproduction number, as well as to account for the generation time, the inverse of the incidence rate, and the infectious period (or removal period), the inverse of the removal rate. The aim is to check whether the relationships the model poses among the various observables are actually found in the data. The study case of the second through the third wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initially the model is tested with reference to the curve of swab-confirmed infectious individuals only. It is found to match the data, if the curve of the removed (that is healed or deceased) individuals is assumed underestimated by a factor of about 3 together with other related curves. Contextually, the generation time and the removal period, as well as the effective reproduction number, are obtained fitting the SIR equations to the data; the outcomes prove to be in good agreement with those of other works. Then, using knowledge of the proportion of Covid-19 transmissions likely occurring from individuals who didn’t develop symptoms, thus mainly undetected, an estimate of the real numbers of the epidemic is obtained, looking also in good agreement with results from other, completely different works. The line of this work is new, and the procedures, computationally really inexpensive, can be applied to any other national or regional case besides Italy’s study case here.

scholarly journals Forecasting Transmission Dynamics of COVID-19 Epidemic in India under Various Containment Measures- A Time-Dependent State-Space SIR Approach

2020 ◽  
Author(s):  
Vishal Deo ◽  
Anuradha Rajkonwar Chetiya ◽  
Barnali Deka ◽  
Gurprit Grover
Keyword(s):  
State Space ◽  
Transmission Rate ◽  
Sir Model ◽  
Primary Objective ◽  
Time Dependent ◽  
Infectious Period ◽  
Total Incidence ◽  
Comparison Results ◽  
Containment Measures ◽  
The Impact

Objectives Our primary objective is to predict the dynamics of COVID-19 epidemic in India while adjusting for the effects of various progressively implemented containment measures. Apart from forecasting the major turning points and parameters associated with the epidemic, we intend to provide an epidemiological assessment of the impact of these containment measures in India. Methods We propose a method based on time-series SIR model to estimate time-dependent modifiers for transmission rate of the infection. These modifiers are used in state-space SIR model to estimate reproduction number R0, expected total incidence, and to forecast the daily prevalence till the end of the epidemic. We consider four different scenarios, two based on current developments and two based on hypothetical situations for the purpose of comparison. Results Assuming gradual relaxation in lockdown post 17 May 2020, we expect the prevalence of infecteds to cross 9 million, with at least 1 million severe cases, around the end of October 2020. For the same case, estimates of R0 for the phases no-intervention, partial-lockdown and lockdown are 4.46 (7.1), 1.47 (2.33), and 0.817 (1.29) respectively, assuming 14-day (24-day) infectious period. Conclusions Estimated modifiers give consistent estimates of unadjusted R0 across different scenarios, demonstrating precision. Results corroborate the effectiveness of lockdown measures in substantially reducing R0. Also, predictions are highly sensitive towards estimate of infectious period.

scholarly journals COVID-19 Case Prediction and Outbreak Control of Navy Cluster in Sri Lanka: Effectiveness of SIR Model

2020 ◽  
Author(s):  
N.W.A.N.Y. Wijesekara ◽  
Nayomi Herath ◽  
K.A.L.C Kodituwakku ◽  
H.D.B. Herath ◽  
Samitha Ginige ◽  
...  
Keyword(s):  
Public Health ◽  
Sri Lanka ◽  
Sir Model ◽  
Epidemiological Surveillance ◽  
Infectious Period ◽  
Base Line ◽  
Ministry Of Health ◽  
Susceptible Population ◽  
Social Distancing ◽  
First Case

Abstract Introduction: Infectious diseases such as coronavirus disease 2019 (COVID-19) can spread dangerously fast in semi-confined places. Nevertheless, it has been found that rapid public health interventions such as isolation and quarantine could successfully curtail such outbreaks. An outbreak of COVID-19 was reported within a cluster of Navy personnel in the Western Province of Sri Lanka commencing from 22nd April 2020. An epidemiological investigation followed by aggressive public health measures were implemented by the Epidemiology Unit of the Ministry of Health with the support of the Sri Lanka Navy in response to the above outbreak. The objective of this research was to predict possible number of cases within the susceptible population in Sri Lanka Navy, to be used primarily for operational planning purpose by the Ministry of Health in control of outbreak in Sri Lanka.Methods: COVID-19 Hospital Impact Model for Epidemics (CHIME) developed by Predictive Health Care Team at Penn Medicine, which was a Susceptibility, Infected and Removed (SIR) model was used. The model was run on 20.05.2020 for a susceptible population of 10400, with number of hospitalized patients on the day of running the model being 357, first case hospitalized on 22.04.2020 and social distancing being implemented on 26.04.2020. Social distancing scenarios of 0, 25, 50 and 74% were run with 10 days of infectious period and 30 days of projection period.Results: With increasing social distancing measures, the peak number of infected persons decreased, as well as the duration of the curve extended. The number of infected cases from the first case ranged from 49th day to 54th day under social distancing scenarios from 0% to 74%. The doubling time increased from 3.1 days to 4.1 days from no social distancing to application of 74% social distancing, with corresponding decrease of Ro from 3.54 to 2.83. Expected daily growth rate of COVID-19 cases has decreased from 25.38 % to 18.53% under aforementioned increasing social distancing scenarios. The observed or actually experienced number of cases were well above the projected number of cases up to 07.05.2020, however, since this date the reported number of cases were lower than the projected number of cases from the model under four social distancing scenarios considered. Similar pattern was noted for the observed or actually experienced number of cases until the 20.05.2020, however, since then it was continuing at a very low intensity until the end of the modelling period. The number of COVID-19 cases prevented as per the model ranged from 2.3 – 21.1 %, compared to the base line prediction of no social distancing. However, based on the observed number of cases and the baseline model with no social distancing, 90.3% reduction was observed by the time of the model application date.Conclusion: The research demonstrated the practical use of a prediction model made readily available through an online open source platform for the operational aspects of controlling a COVID-19 or similar communicable disease outbreaks in a closed community such as armed forces. While comprehensive epidemiological surveillance, contact tracing, case isolation and case management should be the cornerstone of outbreak management, predictive modelling could supplement above efforts.

scholarly journals Mathematical Analysis, Model and Prediction of COVID-19 Data

2020 ◽  
Author(s):  
Yit Chow Tong
Keyword(s):  
Mathematical Analysis ◽  
Interdisciplinary Research ◽  
Sir Model ◽  
Time Varying ◽  
Analysis Model ◽  
Growth Constant ◽  
Future Projections ◽  
Mathematical Procedure ◽  
Discrete Sir Model ◽  
Effective Growth

A simple and effective mathematical procedure for the description of observed COVID-19 data and calculation of future projections is presented. An exponential function E(t) with a time-varying Growth Constant k(t) is used. E(t) closely approximates observed COVID-19 Daily Confirmed Cases with NRMSDs of 1 to 2%. An example of prediction of future cases is presented. The Effective Growth Rates of a discrete SIR model were estimated on the basis of k(t) for COVID-19 data for Germany, and were found to be consistent with those reported in a previous study (1). The proposed procedure, which involves less than ten basic algebraic, logarithm and exponentiation operations for each data point, is suitable for use in promoting interdisciplinary research, exchange and sharing of information.

Coupled Systems of Renewal Equations for Forces of Infection through a Contact Network

2019 ◽  
Vol 63 (3) ◽  
pp. 624-632
Author(s):  
Mahnaz Alavinejad ◽  
Jianhong Wu
Keyword(s):  
General Theory ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Sir Model ◽  
Disease Outbreak ◽  
Discrete Dynamical Systems ◽  
Coupled Systems ◽  
Infectious Period ◽  
Contact Network ◽  
Renewal Equations

AbstractWe formulate a coupled system of renewal equations for the forces of infections in interacting subgroups through a contact network. We use the theory of order-preserving and sub-homogeneous discrete dynamical systems to show the existence and uniqueness of the disease outbreak final sizes in the sub-populations. We illustrate the general theory through a simple SIR model with exponentially and non-exponentially distributed infectious period.

Fitting a Three-Phase Discrete SIR Model to New Coronavirus Cases in New York State

2021 ◽  
Vol 2 (2) ◽  
pp. 59-74
Author(s):  
Kris H. Green
Keyword(s):  
New York ◽  
New York State ◽  
The United States ◽  
Sir Model ◽  
High Fidelity ◽  
Optimal Model ◽  
Training Set ◽  
York State ◽  
Three Phase ◽  
Discrete Sir Model

CDC data on new coronavirus cases in New York State between March 4, 2020 and June 26, 2020 show three distinct phases for the spread of the virus. The authors demonstrate fitting of a simple discrete SIR model with three phases to model these data, achieving a high fidelity to the data. Optimal model fits using both R and Excel are compared, and various issues are discussed. Finally, the model for New York State is treated as a training set for extending and applying the model to the outbreak in other areas of the United States and the country as a whole.

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.

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