scholarly journals Epidemic Overdispersion Strengthens the Effectiveness of Mobility Restrictions

2021 ◽  
Author(s):  
Gerrit Großmann ◽  
Michael Backenköhler ◽  
Verena Wolf
Keyword(s):  
Simulation Study ◽  
Branching Process ◽  
Branching Processes ◽  
Human Mobility ◽  
Transmission Dynamics ◽  
Epidemic Spreading ◽  
Interaction Structure ◽  
Agent Based ◽  
Model Combining ◽  
Spatial Branching Process

AbstractHuman mobility is the fuel of global pandemics. In this simulation study, we analyze how mobility restrictions mitigate epidemic processes and how this mitigation is influenced by the epidemic’s degree of dispersion.We find that (even imperfect) mobility restrictions are generally efficient in mitigating epidemic spreading. Notably, the effectiveness strongly depends on the dispersion of the offspring distribution associated with the epidemic. We also find that mobility restrictions are useful even when the pathogen is already prevalent in the whole population. However, also a delayed implementation is more efficient in the presence of overdispersion. Conclusively, this means that implementing green zones is easier for epidemics with overdispersed transmission dynamics (e.g., COVID-19). To study these relationships at an appropriate level of abstraction, we propose a spatial branching process model combining the flexibility of stochastic branching processes with an agent-based approach allowing a conceptualization of locality, saturation, and interaction structure.

scholarly journals Epidemic Spreading in Urban Areas Using Agent-Based Transportation Models

2019 ◽  
Vol 11 (4) ◽  
pp. 92 ◽  
Author(s):  
Jürgen Hackl ◽  
Thibaut Dubernet
Keyword(s):  
Urban Areas ◽  
Large Scale ◽  
Human Mobility ◽  
Urban Setting ◽  
Disease Spread ◽  
Model Parameters ◽  
Epidemic Spreading ◽  
Agent Based ◽  
Spread Model ◽  
Spread Dynamics

Human mobility is a key element in the understanding of epidemic spreading. Thus, correctly modeling and quantifying human mobility is critical for studying large-scale spatial transmission of infectious diseases and improving epidemic control. In this study, a large-scale agent-based transport simulation (MATSim) is linked with a generic epidemic spread model to simulate the spread of communicable diseases in an urban environment. The use of an agent-based model allows reproduction of the real-world behavior of individuals’ daily path in an urban setting and allows the capture of interactions among them, in the form of a spatial-temporal social network. This model is used to study seasonal influenza outbreaks in the metropolitan area of Zurich, Switzerland. The observations of the agent-based models are compared with results from classical SIR models. The model presented is a prototype that can be used to analyze multiple scenarios in the case of a disease spread at an urban scale, considering variations of different model parameters settings. The results of this simulation can help to improve comprehension of the disease spread dynamics and to take better steps towards the prevention and control of an epidemic.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

scholarly journals Skeletal stochastic differential equations for superprocesses

2020 ◽  
Vol 57 (4) ◽  
pp. 1111-1134
Author(s):  
Dorottya Fekete ◽  
Joaquin Fontbona ◽  
Andreas E. Kyprianou
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Subcritical Case ◽  
Markov Branching Process ◽  
Continuous State ◽  
Common Framework ◽  
Infinite Line ◽  
Current Article ◽  
Lines Of Descent ◽  
Skeletal Representation

AbstractIt is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description of prolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as the skeleton or backbone of the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP).In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever.Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.

Investigating transmission dynamics of influenza in a public indoor venue: An agent-based modeling approach

2021 ◽  
Vol 157 ◽  
pp. 107327
Author(s):  
Yuan Zhou ◽  
Alexander Nikolaev ◽  
Ling Bian ◽  
Li Lin ◽  
Lin Li
Keyword(s):  
Agent Based Modeling ◽  
Transmission Dynamics ◽  
Agent Based ◽  
Modeling Approach

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

Continuity for multi-type branching processes with varying environments

1999 ◽  
Vol 36 (01) ◽  
pp. 139-145 ◽  
Author(s):  
Owen Dafydd Jones
Keyword(s):  
Linear Combination ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Main Tool ◽  
Concentration Function ◽  
Independent Random Variables ◽  
Varying Environments

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ∞). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

On the convergence of the supercritical branching processes with immigration

1977 ◽  
Vol 14 (2) ◽  
pp. 387-390 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Limit Distribution Function ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Supercritical Branching Processes

It is shown for a supercritical branching process with immigration that if the log moment of the immigration distribution is infinite, then no sequence of positive constants {cn} exists such that {Xn/cn} converges in law to a proper limit distribution function F, except for the case F(0 +) = 1. Seneta's result [1] combined with the above-mentioned one imply that if 1 < m < ∞ then the finiteness of the log moment of the immigration distribution is a necessary and sufficient condition for the existence of some constants {cn} such that {Xn/cn} converges in law to a proper limit distribution function F, with F(0 +) < 1.

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