Asymptotic final size distribution of the multitype Reed–Frost process

1986 ◽  
Vol 23 (3) ◽  
pp. 563-584 ◽  
Author(s):  
Gianpaolo Scalia-Tomba
Keyword(s):  
Size Distribution ◽  
Total Population ◽  
Large Population ◽  
Asymptotic Distributions ◽  
Reproduction Rate ◽  
Final Size ◽  
Basic Reproduction Rate ◽  
Infection Pattern ◽  
Large Numbers ◽  
A Chain

The asymptotic final size distribution of a multitype Reed–Frost process, a chain-binomial model for the spread of an infectious disease in a finite, closed multitype population, is derived, as the total population size grows large. When all subgroups are of comparable size, the infection pattern irreducible and the epidemic started by a small number of initial infectives, the classical threshold behaviour is obtained, depending on the basic reproduction rate of the disease in the population, and the asymptotic distributions for small and large outbreaks can be found. The same techniques can then be used to study other asymptotic situations, e.g. small groups in an otherwise large population, large numbers of initial infectives and reducible infection patterns.

Asymptotic final size distribution of the multitype Reed–Frost process

1986 ◽  
Vol 23 (03) ◽  
pp. 563-584
Author(s):  
Gianpaolo Scalia-Tomba
Keyword(s):  
Size Distribution ◽  
Total Population ◽  
Large Population ◽  
Asymptotic Distributions ◽  
Reproduction Rate ◽  
Final Size ◽  
Basic Reproduction Rate ◽  
Infection Pattern ◽  
Large Numbers ◽  
A Chain

The asymptotic final size distribution of a multitype Reed–Frost process, a chain-binomial model for the spread of an infectious disease in a finite, closed multitype population, is derived, as the total population size grows large. When all subgroups are of comparable size, the infection pattern irreducible and the epidemic started by a small number of initial infectives, the classical threshold behaviour is obtained, depending on the basic reproduction rate of the disease in the population, and the asymptotic distributions for small and large outbreaks can be found. The same techniques can then be used to study other asymptotic situations, e.g. small groups in an otherwise large population, large numbers of initial infectives and reducible infection patterns.

The final outcome of an epidemic model with several different types of infective in a large population

1995 ◽  
Vol 32 (3) ◽  
pp. 579-590 ◽  
Author(s):  
Frank Ball ◽  
Damian Clancy
Keyword(s):  
Stochastic Model ◽  
Size Distribution ◽  
Epidemic Model ◽  
Infected Individual ◽  
Large Population ◽  
Asymptotic Distributions ◽  
Initial Population ◽  
Group Model ◽  
Final Size ◽  
Different Types

We consider a stochastic model for the spread of an epidemic amongst a closed homogeneously mixing population, in which there are several different types of infective, each newly infected individual choosing its type at random from those available. The model is based on the carrier-borne model of Downton (1968), as extended by Picard and Lefèvre (1990). The asymptotic distributions of final size and area under the trajectory of infectives are derived as the initial population becomes large, using arguments based on those of Scalia-Tomba (1985), (1990). We then use our limiting results to compare the asymptotic final size distribution of our model with that of a related multi-group model, in which the type of each infective is assigned deterministically.

The final outcome of an epidemic model with several different types of infective in a large population

1995 ◽  
Vol 32 (03) ◽  
pp. 579-590 ◽  
Author(s):  
Frank Ball ◽  
Damian Clancy
Keyword(s):  
Stochastic Model ◽  
Size Distribution ◽  
Epidemic Model ◽  
Infected Individual ◽  
Large Population ◽  
Asymptotic Distributions ◽  
Initial Population ◽  
Group Model ◽  
Final Size ◽  
Different Types

We consider a stochastic model for the spread of an epidemic amongst a closed homogeneously mixing population, in which there are several different types of infective, each newly infected individual choosing its type at random from those available. The model is based on the carrier-borne model of Downton (1968), as extended by Picard and Lefèvre (1990). The asymptotic distributions of final size and area under the trajectory of infectives are derived as the initial population becomes large, using arguments based on those of Scalia-Tomba (1985), (1990). We then use our limiting results to compare the asymptotic final size distribution of our model with that of a related multi-group model, in which the type of each infective is assigned deterministically.

scholarly journals Determining asymptotically large population sizes in insect swarms

2014 ◽  
Vol 11 (99) ◽  
pp. 20140710 ◽  
Author(s):  
James G. Puckett ◽  
Nicholas T. Ouellette
Keyword(s):  
Group Dynamics ◽  
Large Population ◽  
Environmental Cues ◽  
Multi Agent Systems ◽  
Strong Constraint ◽  
Agent Systems ◽  
Self Organized ◽  
Large Numbers ◽  
Population Sizes ◽  
Multi Agent

Social animals commonly form aggregates that exhibit emergent collective behaviour, with group dynamics that are distinct from the behaviour of individuals. Simple models can qualitatively reproduce such behaviour, but only with large numbers of individuals. But how rapidly do the collective properties of animal aggregations in nature emerge with group size? Here, we study swarms of Chironomus riparius midges and measure how their statistical properties change as a function of the number of participating individuals. Once the swarms contain order 10 individuals, we find that all statistics saturate and the swarms enter an asymptotic regime. The influence of environmental cues on the swarm morphology decays on a similar scale. Our results provide a strong constraint on how rapidly swarm models must produce collective states. But our findings support the feasibility of using swarms as a design template for multi-agent systems, because self-organized states are possible even with few agents.

Final size distribution for epidemics

1975 ◽  
Vol 23 (1-2) ◽  
pp. 33-46 ◽  
Author(s):  
Donald Ludwig
Keyword(s):  
Size Distribution ◽  
Final Size

scholarly journals INDEPENDENT ASSOCIATION OF METEOROLOGICAL CHARACTERISTICS WITH INITIAL SPREAD OF COVID-19 IN INDIA

2020 ◽  
Author(s):  
Hemant Kulkarni ◽  
Harshwardhan Vinod Khandait ◽  
Uday Wasudeorao Narlawar ◽  
Pragati G Rathod ◽  
Manju Mamtani
Keyword(s):  
Wind Speed ◽  
Air Temperature ◽  
Meteorological Data ◽  
Reproduction Rate ◽  
The Novel ◽  
Total N ◽  
Mobility Data ◽  
Basic Reproduction Rate ◽  
Independent Association ◽  
Novel Coronavirus

Whether weather plays a part in the transmissibility of the novel COronaVIrus Disease-19 (COVID-19) is still not established. We tested the hypothesis that meteorological factors (air temperature, relative humidity, air pressure, wind speed and rainfall) are independently associated with transmissibility of COVID-19 quantified using the basic reproduction rate (R0). We used publicly available datasets on daily COVID-19 case counts (total n = 108,308), three-hourly meteorological data and community mobility data over a three-month period. Estimated R0 varied between 1.15-1.28. Mean daily air temperature (inversely) and wind speed (positively) were significantly associated with time dependent R0, but the contribution of countrywide lockdown to variability in R0 was over three times stronger as compared to that of temperature and wind speed combined. Thus, abating temperatures and easing lockdown may concur with increased transmissibility of COVID-19.

scholarly journals Nesting ecology of the Pacific cicada killer, Sphecius convallis Patton (Hymenoptera, Crabronidae), in the Sonoran Desert

2020 ◽  
Vol 80 ◽  
pp. 177-191
Author(s):  
Joseph R. Coelho ◽  
Jon M. Hastings ◽  
Charles W. Holliday
Keyword(s):  
Mine Tailings ◽  
Sonoran Desert ◽  
Total Population ◽  
Large Population ◽  
Nesting Ecology ◽  
Factors Affecting ◽  
Population Crash ◽  
The Pacific ◽  
Large Factor ◽  
Provisioning Rate

Factors affecting the ecology of a large population of Pacific cicada killers (Sphecius convallis) occupying a field of mine tailings in Ruby, AZ, were examined. Burrows were quite dense in certain areas around the periphery of the mine tailings, but were dispersed randomly within these areas. Approximately 1600 females (based on burrow counts) and 2500 males (based on mark-recapture) were recorded, yielding a total population estimate of 5000–6000 adults. Female wasps were able to dig much more rapidly in the mine tailings than their congeners S. speciosus in soils from PA, suggesting that the habitat suitability was a large factor in this robust population. Provisioning rate was comparatively slow, however, suggesting that cicada abundance in that year was not a contributor to the high population density. The presence of a sap-producing tree may have eased the energetic and thermoregulatory demands of the wasps. Although excavations revealed that the number of burrows and cells could easily maintain the population size, the lack of cicadas probably resulted instead in a population crash the following season.

scholarly journals An epidemic model with exposure-dependent severities

2005 ◽  
Vol 42 (04) ◽  
pp. 932-949 ◽  
Author(s):  
Frank Ball ◽  
Tom Britton
Keyword(s):  
Branching Process ◽  
Large Population ◽  
Final Outcome ◽  
Model Parameters ◽  
Final Size ◽  
Strong Law ◽  
Sir Epidemic ◽  
Major Outbreak ◽  
Infectious State ◽  
Process Approximation

We consider a stochastic model for the spread of a susceptible–infective–removed (SIR) epidemic among a closed, finite population, in which there are two types of severity of infectious individuals, namely mild and severe. The type of severity depends on the amount of infectious exposure an individual receives, in that infectives are always initially mild but may become severe if additionally exposed. Large-population properties of the model are derived. In particular, a coupling argument is used to provide a rigorous branching process approximation to the early stages of an epidemic, and an embedding argument is used to derive a strong law and an associated central limit theorem for the final outcome of an epidemic in the event of a major outbreak. The basic reproduction number, which determines whether or not a major outbreak can occur given few initial infectives, depends only on parameters of the mild infectious state, whereas the final outcome in the event of a major outbreak depends also on parameters of the severe state. Moreover, the limiting final size proportions need not even be continuous in the model parameters.

The Demographic Transition Theory of War: Why Young Societies Are Conflict Prone and Old Societies Are the Most Peaceful

2019 ◽  
Vol 43 (3) ◽  
pp. 53-95 ◽  
Author(s):  
Deborah Jordan Brooks ◽  
Stephen G. Brooks ◽  
Brian D. Greenhill ◽  
Mark L. Haas
Keyword(s):  
Young People ◽  
Total Population ◽  
Empirical Examination ◽  
Demographic Transitions ◽  
The Road ◽  
Large Numbers ◽  
The World ◽  
Theory Of War ◽  
First Time

The world is experiencing a period of unprecedented demographic change. For the first time in human history, marked disparities in age structures exist across the globe. Around 40 percent of the world's population lives in countries with significant numbers of elderly citizens. In contrast, the majority of the world's people live in developing countries with very large numbers of young people as a proportion of the total population. Yet, demographically, most of the world's states with young populations are aging, and many are doing so quickly. This first-of-its kind systematic theoretical and empirical examination of how these demographic transitions influence the likelihood of interstate conflict shows that countries with a large number of young people as a proportion of the total population are the most prone to international conflict, whereas states with the oldest populations are the most peaceful. Although societal aging is likely to serve as a force for enhanced stability in most, and perhaps all, regions of the world over the long term, the road to a “demographic peace” is likely to be bumpy in many parts of the world in the short to medium term.

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