Matching Items (2)

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Prey-predator-parasite: an ecosystem model with fragile persistence

Description

Using a simple $SI$ infection model, I uncover the

overall dynamics of the system and how they depend on the incidence

function. I consider both an epidemic and endemic perspective of the

model,

Using a simple $SI$ infection model, I uncover the

overall dynamics of the system and how they depend on the incidence

function. I consider both an epidemic and endemic perspective of the

model, but in both cases, three classes of incidence

functions are identified.

In the epidemic form,

power incidences, where the infective portion $I^p$ has $p\in(0,1)$,

cause unconditional host extinction,

homogeneous incidences have host extinction for certain parameter constellations and

host survival for others, and upper density-dependent incidences

never cause host extinction. The case of non-extinction in upper

density-dependent

incidences extends to the case where a latent period is included.

Using data from experiments with rhanavirus and salamanders,

maximum likelihood estimates are applied to the data.

With these estimates,

I generate the corrected Akaike information criteria, which

reward a low likelihood and punish the use of more parameters.

This generates the Akaike weight, which is used to fit

parameters to the data, and determine which incidence functions

fit the data the best.

From an endemic perspective, I observe

that power incidences cause initial condition dependent host extinction for

some parameter constellations and global stability for others,

homogeneous incidences have host extinction for certain parameter constellations and

host survival for others, and upper density-dependent incidences

never cause host extinction.

The dynamics when the incidence function is homogeneous are deeply explored.

I expand the endemic considerations in the homogeneous case

by adding a predator into the model.

Using persistence theory, I show the conditions for the persistence of each of the

predator, prey, and parasite species. Potential dynamics of the system include parasite mediated

persistence of the predator, survival of the ecosystem at high initial predator levels and

ecosystem collapse at low initial predator levels, persistence of all three species, and much more.

Contributors

Agent

Created

Date Created
  • 2017

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Study of an epidemic multiple behavior diffusion model in a resource constrained social network

Description

In contemporary society, sustainability and public well-being have been pressing challenges. Some of the important questions are:how can sustainable practices, such as reducing carbon emission, be encouraged? , How can

In contemporary society, sustainability and public well-being have been pressing challenges. Some of the important questions are:how can sustainable practices, such as reducing carbon emission, be encouraged? , How can a healthy lifestyle be maintained?Even though individuals are interested, they are unable to adopt these behaviors due to resource constraints. Developing a framework to enable cooperative behavior adoption and to sustain it for a long period of time is a major challenge. As a part of developing this framework, I am focusing on methods to understand behavior diffusion over time. Facilitating behavior diffusion with resource constraints in a large population is qualitatively different from promoting cooperation in small groups. Previous work in social sciences has derived conditions for sustainable cooperative behavior in small homogeneous groups. However, how groups of individuals having resource constraint co-operate over extended periods of time is not well understood, and is the focus of my thesis. I develop models to analyze behavior diffusion over time through the lens of epidemic models with the condition that individuals have resource constraint. I introduce an epidemic model SVRS ( Susceptible-Volatile-Recovered-Susceptible) to accommodate multiple behavior adoption. I investigate the longitudinal effects of behavior diffusion by varying different properties of an individual such as resources,threshold and cost of behavior adoption. I also consider how behavior adoption of an individual varies with her knowledge of global adoption. I evaluate my models on several synthetic topologies like complete regular graph, preferential attachment and small-world and make some interesting observations. Periodic injection of early adopters can help in boosting the spread of behaviors and sustain it for a longer period of time. Also, behavior propagation for the classical epidemic model SIRS (Susceptible-Infected-Recovered-Susceptible) does not continue for an infinite period of time as per conventional wisdom. One interesting future direction is to investigate how behavior adoption is affected when number of individuals in a network changes. The affects on behavior adoption when availability of behavior changes with time can also be examined.

Contributors

Agent

Created

Date Created
  • 2013