presentation 110811

8/3/2019 Presentation 110811

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BY: KATHARINE F. PREEDY, PIETA G. SCHOFIELD, MARK A. J.CHAPLAIN, AND STEPHEN F. HUBBARD

PRESENTED BY : JORGE REYES-SILVEYRA, OLEG KOLGUSHEV, &RAVI SHANKER PANDEY

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Disease Induced dynamics in

host parasitoid systems: chaosand coexistence


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INTRODUCTION

Host parasitoid systemHost: An organism that harbors a parasite by

providing nourishment and shelter.

Parasitoid: are insects whose larvae develop byfeeding on a single host and spends a significantportion of its life attached to or within hostorganism

Parasite vs. Parasitoid: Parasitoids are similar toparasites except that they sterilizes or kill andsometimes consumes, the host.


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INTRODUCTION

Classification of Parasitoids:

Idiobionts: Immobilize or kill their host at the time

of oviposition.

Koinobionts: Let the host alive till juvenileparasitoids emerge from their eggs.

Why to study parasitoids?


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INTRODUCTION

Host-parasitoids are subject to disease also, butvery few modeling has been done to addressdynamics of Host-parasitoid-pathogen interaction.

Transmission of Disease:Horizontally: being in contact with infected host,

dirty needle effect.

Vertically: through infection of eggs from aninfected mother.


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INTRODUCTION

The effect of such infections are simulated bymathematical model by introducing disease dynamicsinto a model system of two parasitoids attacking a singlehost species.

In this model they have analyzed:steady state of model and their stability.Transient dynamics

Spatio-temporal dynamics: random motility has beenincluded to examine spatial effects in host-parasitoidsdue to their movement in given domain.


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MODEL

Two Versions: With and without host infection.Both:

2 Species of parasitoids (P1 and P2)

1 Type of Host (H)Parasites death rates (d1,d2), host growth rate (r) and

carrying capacity (K) is same in both.

Handling time is a function of the form (1-e-H)

determines the efficiency of parasitoids to infect hostIvlev or Holling type II functional response


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If a population of consumers feeds on limited resources, then the change in

individual consumption with change in resource density will be dh(1-e-H)

Ivlev or Holling type II functional response


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Parasites death rates (d1,d2), host growth rate (r) andcarrying capacity (K)

Infection capacity rates (1 and 2)

New generation of parasites in host (e1 and e3)

Steady states (0,0,0),(K,0,0),(H,0,P2),(H,P1,0)

Not (H,P1,P2)

FIRST MODEL


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Inclusion of hostinfection into the system.

Uninfected (hu) andinfected (hi) hosts

Mortality rate of infectedhost ()

Transmissibility betweenuninfected and infectedhosts ()

SECOND MODEL


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t=rt,hu=(hu/K),hi=(hi/K), P1=(P1/K) andP2=(P2/K)

In the model:si=i/rpi=i*K

v=K/rci=((ei*i)/r)i=di/r

NON DIMENSIONAL: SECOND MODELMODIFIED


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SECOND MODEL MODIFIED CASES

Case 1:

(0,0,0,0), (1,0,0,0), (0,hi,0,0), (hi,hu,0,0),(0,hi,0,P2), (hu,0,0,P2), (hu,0,P1,0), (o,hi,P1,0),(hu,hi,P1,P2)

In the absence of one species of parasitoid theinfected or uninfected host become extinct

If Infection is omitted, then weaker parasitoid

goes extinctBig oscilations, high amplitude at beginning


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SECOND MODEL MODIFIED CASE 1


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Case 2:

Change infection rate(v) and death rates(1, 2)

Conversion point is an unstable spiral (no

convergence)


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Case 3:

Increase v

Increased amplitude oscillations and frequency

After 50,000 steps system does not stabilize

Fixed point is not stable either


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SPATIO-TEMPORAL DYNAMICS

Temporal model the system createsunstable/chaotic regions in the solution.

Movement in space need to beconsidered.

For simplicity, one dimensional boundedspace is used (0,L)

D are random motility coefficients:D1 = D2 = 8 * 10

-7

D3 = D4 = 7.5 * 10-6

Diffusion of host is slower that diffusionof parasitoid in this model

Equal diffusion creates similar solutionsas in ODE


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Initially, a wave of uninfected hostsclosely followed waves of P1.4b) P2 leads a wave train throughthe domain. In the absence ofinfection P2 can not compete anddrops to low levels. 4c) we see richDynamics associated with thetransient phase of ODE withhigh-frequency, large amplitude

oscillations. 4d,e,f) as the hostinfection invades, P2 follows it and the oscillations slow down and rapidly decrease in amplitude and thesystem has reached its steady state. The transient oscillations in the healthy host population mean that theinfection is not invading a homogeneous population and the wave of invasion is disrupted. The order ofinvasion can be explained by the fact that parasitoids require hosts to reproduce and hence cannot existwithout them, so the hosts must invade first. The infection invades at a slower speed than both the healthyhosts and the parasitoids P1. Similarly, P2 has a very low rate of population growth in the absence of infectionand it does not invade until the infection has established itself.


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5a) as in Figure 2, we seea travelling wave of healthy

hosts followed closely bya travelling wave of P1 andP2. 5b) P2 cannot competeand we see a longer periodof transient dynamics.5c) the disruption of wavesof infection is extreme here.

It does not follow a wave-front,but reaches low levels throughout the domain before rising to a peak and spreading out from it. 5d) P2cannot compete in the absence of infection, so its population density increases behind the peak of infectionand it takes much longer to become established. 5e) the oscillations decrease in amplitude, but this istemporary and the amplitude increases slightly again. 5f) the long-term dynamics of ODE are a stable limitcycle, and in the PDE, we see persistent rich spatiotemporal heterogeneity. This type of behavior has beenobserved in previous work examining predatorprey systems and hostparasitoid systems.


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The rate of infection isHigher and the populationP2, becomes establishedmore quickly.

The peaks in host infectionseen in figure 3a,b do not

occur when diffusion isintroduced to the system,but we do see pulses of fastoscillations and as can be seen from figure 6f, the infection level continues to vary widely bothspatially and temporally. The complex spatiotemporal dynamics seen in figure 5 are very muchin evidence here with larger oscillations and a greater degree of spatiotemporal heterogeneity.


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DISCUSSION

Theoretical model has been developed to addressthe effect of disease in host-parasitoids system.Two parasitoids are included in system, that proved

to be useful in avoiding extinction of system.Horizontally as well as vertically transmission has

been included, but they did not study the effect ofvarying vertical transmission parameter.

Although disease is detrimental, yet it allows forcoexistence of all species, which was not possible insimple host-parasitoids system


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DISCUSSION

As disease indirectly benefits the less efficientcompetitor, which become extinct in the absence ofdisease.The finding of co-existence in presence of disease is in

contrast to previous findings, as shared host led toextinction of one of the parasitoid.Three cases were studied, by varying only infection rates

and relative death rate.

For spatio-temporal dynamics, they have not consideredthe case of aggregation at locations of high chemicalcues.


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DISCUSSION

If parasitoids were removed from system?

Transient dynamics suggest that throughdisturbance initial conditions can be achieved and

by varying the parameters, it can be extended.Due to this, the region where there is regular

disturbance it will never achieve steady state.

This model could be applied to predator-prey-pathogen interactions.


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DISCUSSION

Removal of any detrimental agent(to host), maylead to the loss of other detrimental agents insystem. This can help in study of disease dynamics

and treatment of pathogenic infection


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Thanks

presentation 110811

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