Plant Pathogen and Hyperparasite Annual Cycle

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initial pathogen density

0.001

initial hyperparasite density

0.0001

pathogen infection rate

0.1

hyperparasite infectiousness

0.1

This Demonstration shows the annual cycle of a population of a plant pathogen that is itself attacked by a hyperparasite. The pathogen increases at a per capita rate that is reduced in proportion to the population size and decreases during the season as conditions become progressively unfavorable. It is destroyed by a hyperparasite at a rate that is proportional to both populations. The growing season is assumed to be 180 days. The hyperparasite harms the pathogen and multiplies by destroying it, but has no in-season death rate. This models something with long-lived structures but only one food source.

Details

If the pathogen population as a proportion of its maximum is

h

and the population of the hyperparasite is

s

, and both are functions of time

t

, the equations governing the changes in time are:

dh

dt

=

r

h

h(t)(1-h(t))(1-t)-bh(t)s(t)

,

ds

dt

=bh(t)s(t)

, and

h(0)=

h

0

,

s(0)=

s

0

.

Permanent Citation

Michael Shaw

"Plant Pathogen and Hyperparasite Annual Cycle"
http://demonstrations.wolfram.com/PlantPathogenAndHyperparasiteAnnualCycle/
Wolfram Demonstrations Project
Published: March 7, 2011