scholarly journals Relating the Progeny Production Curve to the Speed of an Epidemic

2013 ◽  
Vol 103 (3) ◽  
pp. 204-215 ◽  
Author(s):  
Francis J. Ferrandino
Keyword(s):  
Theoretical Models ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Progeny Production ◽  
A Value ◽  
Order Expansion ◽  
Mckendrick Equation ◽  
Temporal Moments ◽  
Production Curve ◽  
Mean Time

The dependence of the initial infection rate, r, on the basic reproductive number, R0, and the temporal moments of the progeny production curve are examined. A solution to the linearized Kermack-McKendrick equation is presented and used to analyze a variety of theoretical models of pathogen reproduction. The solution yields a relation between r and the basic reproductive number, R0; the mean time between pathogen generations, μ; and the standard deviation about this mean, σ. A transformation using the dimensionless variables rμ and rσ is introduced, which maps the solution onto a one-dimensional curve. An approximation for the value of r in terms of R0 and the first four temporal moments of the reproductive curve is derived. This allows direct comparison of epidemics resulting from theoretical models with those generated using experimentally obtained reproduction curves. For epidemics characterized by a value of rμ < 5, the value of r is well determined (<2%) by this fourth-order expansion regardless of the functional form of the reproduction curve.

scholarly journals ESTIMATION OF THE VALUE OF THE COVID-19 BASIC REPRODUCTIVE NUMBER AND THE EFFECT OF ANTI-EPIDEMIC MEASURES AND “SEASONAL FACTOR” ON THIS VALUE

2021 ◽  
Vol 18 (38) ◽  
pp. 149-163
Author(s):  
Andrey GERASIMOV ◽  
Irina SEMENYCHEVA ◽  
Olga BELAIA ◽  
Elena VOLCHKOVA ◽  
Andrey GOROBCHENKO
Keyword(s):  
Accurate Method ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Reproduction Rate ◽  
Infected People ◽  
Noticeable Increase ◽  
A Value ◽  
Health Authorities ◽  
Seasonal Factors ◽  
Seasonal Factor

Background: The emergence of COVID-19 has led to increased attention to mathematical models of epidemiology, one of the main parameters of which is the basic reproductive number R0. Its value determines both the dynamics of the incidence and the level of anti-epidemic measures. Therefore, it is desirable to have a fairly accurate method for assessing R0 for each day. Aim: Develop a methodology for determining the R0 value for COVID-19, taking into account a reasonably rapid and significant change in its value over time. Methods: a method for calculating reproduction number R0 was proposed for assessing COVID-19 R0, taking into account the change in the contagiousness of the infected people during the infectious process. Results and Discussion: In Russia in June-August 2020, the reproduction rate was slightly less 1, but in September R0 began to grow, exceeded 1, which was caused a noticeable increase in the incidence. During June in Brazil, R0 stabilized at a value of 1. The activity of transmission of the pathogen is influenced by seasonal changes in the reproduction rate R0 and the level of community immune status. Based on the assessment of the dynamics of the incidence of other pneumonia, it was found that the change of R0 during the year is about 10%, with a minimum in summer. Conclusions: while maintaining the current activity of anti-epidemic measures due to seasonal factors of the activity of the transmission mechanism and accumulation of the immune individuals in the coming months, the situation in the Russian Federation will worsen with an increase in the incidence doubled within six months, and in Brazil in six months — improve with a decrease in the incidence ten times. However, the dynamics of the incidence will be determined primarily by the work of the administration and health authorities and the conscientiousness of citizens.

The Social Neuroscience of Cooperation

2018 ◽  
Author(s):  
Jay Joseph Van Bavel
Keyword(s):  
Theoretical Models ◽  
Brain Regions ◽  
Review Literature ◽  
Social Neuroscience ◽  
Future Research ◽  
A Value ◽  
Group Cooperation ◽  
Neural Processes ◽  
The Social ◽  
Cooperative Decision Making

We review literature from several fields to describe common experimental tasks used to measure human cooperation as well as the theoretical models that have been used to characterize cooperative decision-making, as well as brain regions implicated in cooperation. Building on work in neuroeconomics, we suggest a value-based account may provide the most powerful understanding the psychology and neuroscience of group cooperation. We also review the role of individual differences and social context in shaping the mental processes that underlie cooperation and consider gaps in the literature and potential directions for future research on the social neuroscience of cooperation. We suggest that this multi-level approach provides a more comprehensive understanding of the mental and neural processes that underlie the decision to cooperate with others.

scholarly journals Dynamics analysis of an online gambling spreading model on scale-free networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Kong ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Xinming Cheng ◽  
He Wang ◽  
...  
Keyword(s):  
Network Topology ◽  
Negative Impact ◽  
Online Gambling ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Scale Free ◽  
Spreading Model ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

scholarly journals Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamid Khataee ◽  
Istvan Scheuring ◽  
Andras Czirok ◽  
Zoltan Neufeld
Keyword(s):  
Mobile Phone ◽  
Basic Reproductive Number ◽  
Mobile Phone Data ◽  
Reproductive Number ◽  
Expansion Phase ◽  
Social Distancing ◽  
Exponential Expansion ◽  
Total Death ◽  
Mobility Reduction ◽  
Epidemiological Parameters

AbstractA better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ($$R_0$$ R 0 ) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

scholarly journals Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1164
Author(s):  
Weiwei Ling ◽  
Pinxia Wu ◽  
Xiumei Li ◽  
Liangjin Xie
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Control Strategy ◽  
Theoretical Basis ◽  
Dynamic Properties ◽  
Transmission Mechanism ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Vector Borne ◽  
Citrus Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

scholarly journals Effect of specific non-pharmaceutical intervention policies on SARS-CoV-2 transmission in the counties of the United States

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bingyi Yang ◽  
Angkana T. Huang ◽  
Bernardo Garcia-Carreras ◽  
William E. Hart ◽  
Andrea Staid ◽  
...  
Keyword(s):  
United States ◽  
Home Visiting ◽  
Leisure Activities ◽  
The United States ◽  
Causal Effects ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
County Level ◽  
Metapopulation Model ◽  
Pharmaceutical Interventions

AbstractNon-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (Reff) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median Reff below 1 when combined with either stay at home orders (median Reff 0.97, 95% confidence interval (CI) 0.58–1.39) or face masks (median Reff 0.97, 95% CI 0.58–1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

scholarly journals Viral Dynamics of Acute HIV-1 Infection

1999 ◽  
Vol 190 (6) ◽  
pp. 841-850 ◽  
Author(s):  
Susan J. Little ◽  
Angela R. McLean ◽  
Celsa A. Spina ◽  
Douglas D. Richman ◽  
Diane V. Havlir
Keyword(s):  
Antiretroviral Therapy ◽  
Hiv Infection ◽  
Doubling Time ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Target Cells ◽  
Viral Dynamics ◽  
Acute Hiv Infection ◽  
Acute Hiv ◽  
The Mean

Viral dynamics were intensively investigated in eight patients with acute HIV infection to define the earliest rates of change in plasma HIV RNA before and after the start of antiretroviral therapy. We report the first estimates of the basic reproductive number (R0), the number of cells infected by the progeny of an infected cell during its lifetime when target cells are not depleted. The mean initial viral doubling time was 10 h, and the peak of viremia occurred 21 d after reported HIV exposure. The spontaneous rate of decline (α) was highly variable among individuals. The phase 1 viral decay rate (δI = 0.3/day) in subjects initiating potent antiretroviral therapy during acute HIV infection was similar to estimates from treated subjects with chronic HIV infection. The doubling time in two subjects who discontinued antiretroviral therapy was almost five times slower than during acute infection. The mean basic reproductive number (R0) of 19.3 during the logarithmic growth phase of primary HIV infection suggested that a vaccine or postexposure prophylaxis of at least 95% efficacy would be needed to extinguish productive viral infection in the absence of drug resistance or viral latency. These measurements provide a basis for comparison of vaccine and other strategies and support the validity of the simian immunodeficiency virus macaque model of acute HIV infection.

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