Epidemics on networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Sir Model ◽  
Disease Outbreak ◽  
Time Dependent ◽  
Configuration Model ◽  
Static Properties ◽  
Sis Model ◽  
Percolation Process ◽  
Dependent Behavior ◽  
Si Model ◽  
Number Of Individuals

This chapter discusses the spread of diseases over contact networks between individuals and the methods used to model this process. The chapter begins with an introduction to the classic models of mathematical epidemiology, including the SI model, the SIR model, and the SIS model. Models for coinfection and competition between diseases are also discussed, as well as “complex contagion” models used to represent the spread of information. The remainder of the chapter deals with the behavior of these models on networks, where the behavior of spreading diseases depends strongly on network structure. It is shown that the SIR model maps to a bond percolation process on networks, allowing us to solve for static properties such as the total number of individuals infected in a disease outbreak. The case of the configuration model is developed in detail and the calculations are extended to competing diseases, coinfection, and complex contagion. Time-dependent behavior of diseases on networks is also studied using various differential equation approximations, including pair approximations and degree-based approximations.

scholarly journals Flattening the Curve: The effects of intervention strategies during COVID-19

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Kelly Reagan ◽  
Rachel Pryor ◽  
Gonzalo Bearman ◽  
David Chan
Keyword(s):  
Personal Protective Equipment ◽  
Transmission Rate ◽  
State Level ◽  
Sir Model ◽  
Intervention Strategies ◽  
Time Dependent ◽  
Protective Equipment ◽  
Social Distancing ◽  
Peak Number ◽  
Number Of Individuals

COVID-19 has plagued countries worldwide due to its infectious nature. Social distancing and the use of personal protective equipment (PPE) are two main strategies employed to prevent its spread. A SIR model with a time-dependent transmission rate is implemented to examine the effect of social distancing and PPE use in hospitals. These strategies’ effect on the size and timing of the peak number of infectious individuals are examined as well as the total number of individuals infected by the epidemic. The effect on the epidemic of when social distancing is relaxed is also examined. Overall, social distancing was shown to cause the largest impact in the number of infections. Studying this interaction between social distancing and PPE use is novel and timely. We show that decisions made at the state level on implementing social distancing and acquiring adequate PPE have dramatic impact on the health of its citizens.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

Time-dependent behavior of nitric oxide excited states under the effect of electron impact

2021 ◽  
Vol 28 (2) ◽  
pp. 024503
Author(s):  
Mohammed amin Ferdi ◽  
Abdelaaziz Bouziane ◽  
Mourad Djebli
Keyword(s):  
Nitric Oxide ◽  
Electron Impact ◽  
Excited States ◽  
Time Dependent ◽  
Dependent Behavior

Time-dependent behavior of retaining piles during pre-excavation dewatering in multi-layered saturated soils

2021 ◽  
Vol 137 ◽  
pp. 104300
Author(s):  
Yi Chong Cheng ◽  
Ri Hong Zhang ◽  
Kui Hua Wang ◽  
Zhi Yong Ai
Keyword(s):  
Time Dependent ◽  
Saturated Soils ◽  
Dependent Behavior

The flow properties of honey–malt spread

2017 ◽  
Vol 23 (5) ◽  
pp. 415-425 ◽  
Author(s):  
M Dianat ◽  
M Taghizadeh ◽  
F Shahidi ◽  
SMA Razavi
Keyword(s):  
Flow Behavior ◽  
Time Dependent ◽  
Malt Extract ◽  
Barley Malt ◽  
First Order ◽  
Dependent Behavior ◽  
Thixotropic Behaviour ◽  
Order Stress ◽  
Temperature Levels ◽  
Independent Behavior

In this study, the effect of barley malt extract at two brix levels (74 and 79 °Bx) and three ratios of malt extract/honey (65:35, 70:30 and 75:25) on the flow behavior properties of honey–malt spread at three temperature levels (35 ℃, 45 ℃ and 55 ℃) was investigated. Time-dependent behavior data of the spread samples were appropriately fitted to the Weltman, first-order stress decay with a zero stress value and first-order stress decay with a non-zero stress value models. Also, the Power-law, Herschel–Bulkley, Casson and Bingham models were used for curve fitting the time-independent behavior data. Regarding the R2 and root mean square error coefficients, the first-order stress decay with a non-zero stress value and Herschel–Bulkley models were selected as the suitable models to describe the flow behavior of samples. The results for time-dependent properties showed that spread samples exhibit a thixotropic behaviour, as the viscosity for all samples decreased with increase in shearing time at a constant shear rate of 50 s−1.

Time-Dependent Behavior and Fracture of Functionally Graded Thermal Barrier Coatings under Thermal Shock

2005 ◽  
Vol 492-493 ◽  
pp. 379-384 ◽  
Author(s):  
Klod Kokini ◽  
Sudarshan V. Rangaraj
Keyword(s):  
Thermal Shock ◽  
Thermal Barrier Coatings ◽  
Functionally Graded ◽  
Yttria Stabilized Zirconia ◽  
Time Dependent ◽  
Thermal Barrier ◽  
Stabilized Zirconia ◽  
Barrier Coatings ◽  
Dependent Behavior ◽  
Bond Coat Alloy

The thermal fracture and its dependence on time-dependent behavior in functionally graded yttria stabilized zirconia - NiCoCrAlY bond coat alloy thermal barrier coatings was studied. The response of three coating architectures of similar thermal resistance to laser thermal shock tests was considered, experimentally and computationally.

scholarly journals Time Dependent Behavior of Soft Rock and Its Essential Interpretation.

1998 ◽  
pp. 1-10 ◽  
Author(s):  
Toshihisa Adachi ◽  
Fusao Oka ◽  
Hiroshi Soraoka ◽  
Masashi Koike
Keyword(s):  
Soft Rock ◽  
Time Dependent ◽  
Dependent Behavior
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