A two-phase epidemic driven by diffusion

Reluga, Tim

doi:10.1016/s0022-5193(04)00138-9

Cited by 10 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we expect that anomalous invasion dynamics could occur in viruses or microbial systems, partic-345 ularly infectious diseases, where hosts constitute demes within a large local population. Indeed, anomalous invasion speeds have been shown to occur in SIR-type systems that allow "virus shedding" which allow the production of virions proportional to infected agents (Reluga, 2004). RNA viruses can have mutation rates as high as 10 −3 -10 −5 per base pair per generation (Drake et al, 1998), and can exist at densities of 10 12 individuals per gramme of human faeces (Atmar et al,350 2008), so within-host populations could easily be high enough for anomalous invasion speeds.…”

Section: Discussionmentioning

confidence: 99%

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Keenan

Cornell

2020

Preprint

View full text Add to dashboard Cite

Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life history theory predicts that reproductive fitness -another key determinant of invasion dynamics -may be lower for more dispersive strains. Here, we use a mathematical 5 model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be "anomalous" (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the 10 traits of at most two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary or epidemiological invasions.

show abstract

Section: Discussionmentioning

confidence: 99%

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Keenan

Cornell

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…It will turn out that the appropriate theoretical framework will be graph theory where each vertices of the graph will be thought as the cities and the edges the lines of transportation. In a first approximation, we will assume that infected populations are only subject to spatial diffusion along the lines, as it is traditionally assumed in classical spatial SIR models [1,3,9,22]. As a consequence, in our model, the dynamics of the epidemic only takes place in the cities.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of epidemic spreading on connected graphs

Besse¹,

Faye²

2020

Preprint

View full text Add to dashboard Cite

We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex. We describe the main properties of the system, and also derive the final total population of infected individuals. We present a semi-implicit in time numerical scheme based on finite differences in space which preserves the main properties of the continuous model such as the uniqueness and positivity of solutions and the conservation of the total population. We also illustrate our results with a selection of numerical simulations for a selection of connected graphs.

show abstract

“…Typically the model is the reaction-diffusion equation. Originating in chemistry, these are widely used in ecology (Holmes, et al, 1994) and have been adapted to epidemics (Kendall, 1965;Noble, 1974;Mollison, 1977;Murray, Stanley and Brown, 1986;Lopez, et al, 1999;Reluga, 2004). They incorporate the features of the SIR model that explain the course of an epidemic over time and add the term u xx + u yy , the sum of the second partial derivatives of change in two spatial dimensions, to model diffusion.…”

Section: Introductionmentioning

confidence: 99%

Geographical Distributions and Spatial Equilibrium in Historical Epidemics of the United States

Coleman

2018

Preprint

View full text Add to dashboard Cite

This research examines the geographical distributions of several historical epidemics in the United States and investigates whether they reached a geographical equilibrium, however briefly. An equilibrium distribution over a geographical area, as the end state of a diffusion or spatial contagion process, has definitive mathematical properties. These permit qualitative and quantitative tests that may confirm an equilibrium and identify its characteristics. The analysis uses United States state-level data for several common infectious diseases of the 1950s, and results show geographical equilibrium distributions for several epidemics. These are not predicted by the most commonly used epidemiological models but are consistent with observed geographical disparities in disease prevalence that continued over a number of years in spite of recurrent epidemic cycles and long-term trends.

show abstract

A two-phase epidemic driven by diffusion

Cited by 10 publications

References 0 publications

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Dynamics of epidemic spreading on connected graphs

Geographical Distributions and Spatial Equilibrium in Historical Epidemics of the United States

Contact Info

Product

Resources

About