“To cull or not to cull, this is the problem”:

undersired effects of animals removal to eraticate diseases in widlife populations

(the adaptive dynamics of CSF in wild boars)

EEE - ICTP

Trieste April 13-15 2005

Giulio De LeoDipartimento di Scienze Ambientali

Università degli Studi di Parma - Italy

Thanks to A.Dobson and M. Pascualand to the NCEAS WG on Seasonality and Infectious diseases

cIIISI

cSISSGSo

o

)( c :hunting rate [t-1]

If the case of no culling (c=0):

Let’s take the Classical Swine Fever (CSF) as a reference disease

K

R0

10 R

TKK

It can be proven that it is possible to eradicate the disease if: c > r [1- 1/Ro]

Basics of Classical swine fever (CSF) or Hog Cholera

• A highly contagious disease due to a RNA virus, Family TOGAVIRIDAE, Genus Pestivirus;

• It is a List A disease in the OIE Classification of Diseases

• Suidae are the sole natural hosts;

Basics of Classical swine fever (CSF) or Hog Cholera

• Infected animals may shed large amounts of virus for 20 - 40 days through oronasal and lacrimal secretions, urine and feces

• The direct contact between infected and susceptible animals is the principle means of viral transmission;

Basics of Classical swine fever (CSF) or Hog CholeraEpidemiology

• CSF causes high morbidity and mortality (up to 90%) during the first epidemic wave…

but low virulent strains can be isolated in wild boars in the following endemic phase;– Acute infections – Chronic infections /endemic phases

CSF distribution(OEI 1995-1997)

CSF outbreaks in wild boars1990-2001

Why people care about CSF in EU?

• Wild boars are blamed to be the reservoir of CSF

UE Damages from CSF between 1993 and 2000

Country N. Swines removed (        = 1 milion specimen)

                  

NL                                                                                                                                 10

                  

Germany                           2

                  

Spaain              1

                  

Belgium           < 1

                  

Italy           < 1

A 100 kg pig ~ €150,00

• which is easier to say than to do it…

• The EU supports a program to eradicate the virus from wild boar mainly based on reducing population density through culling

– What to cull?

– Where to cull?

– When to cull?

– How to cull?

0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

Culling rate [y-1]

tras

mis

sion

rat

es

c( )

a c( )

c

.

Culling rate [y-1]

Drawbacks of culling (1/2)as reported by the Italian Wildlife National Service (INFS)

• It may push hosts out of their natural home range, thus fostering disease spread

~ 20% increase of culling rate

~ 60% reduction of population density

with respect to constant

Ro

Culling rate [y-1]

0 0.1 0.2 0.3 0.4 0.50

2

4

6reproduct ive number

Cuilling Rate

1

Ro c( )

Rao c( )

ca ce

c

ce caca

18 .9%

.

Seq ce( )

K8.8%

Seq 0( )

K21 .7%

Saeq ca( )

K23 .3%

1

Drawbacks of culling (2/2)• It may push hosts out of their natural

home range, thus fostering disease spread• If culling is focused mainly on old (low susceptible)

hosts, it may change population age structure in favor of more susceptible yearlings

• Given the existence of multiple strains of CSF (Biagetti et al. 2001), a change in host density may foster the selection of less virulent but more persistent strains, thus making culling more costly and ineffective

• Research questions:– Is it possible? – If positive, under which conditions?– Which are the consequences?

A simple two-strains competition model

• Hosts I1 infected

with a Low Virulent Strain (LVS)

small 1

• Hosts I2 infected

with a High Virulent Strain (HVS) large 2

S

I2

I1

low virulent strain

(small 1)

highly virulent strain

(large 2)

c

cc

12 is the super-infection

coefficient

The new equations (LVS vs. HVS ):

S' =G(S) - 1I1S - 2I2S - cS

I1' = 1I1S - (1 + + c) I1 12I1I2

I2' = 2I2S - (2 + + c) I2 + 12I1I2

Assumptions on the LVS vs. HVS

• Disease induced mortality (virulence)

• 1 << 2

• Transmission rate

• 1 2 12 0

Basic epidemiological implications of the above assumptions

• Basic Reproductive rate (LVS vs. HVS)

R01 =

1K

1 + >

2K

2 + = R02

• Threshold density for disease eradication

KT1< KT2

LVS can persist in a very sparse population

Su

scep

tib

les (

S)

(over 2

20

km2 )

0

100

200

300

400

time [month]

0 20 40 60 80 100

In

fecte

d (

I)

0

25

50

75

100

S

I1I2

time [month]

0 5 10 15 20

0 5 10 15 20

In

fecte

d (

I)

0.1

1

10

100

I1

I2

(LVS)

(LVS)

(HVS)

(HVS)

Further epidemiological implications

• If there is no super-infection (12=0)

LVS always outcompetes HVS

If there is super-infection (12 >0)

12 <

1 KT

I*1

• If LVS outcompetes HVS

12 >

2 KT

I*2

• If HVS outcompetes LVS

1 KT

I*1

<12<

2 KT

I*2

• If LVS and HVS coexist

KT = KT2 – KT1 – c (1/1 – 1/2)

I*1 =

G(KT1+ c/1)

1 (K T1+ c/1) - c/1 I*

2 = G(KT2 + c/2)

2 (KT2+ c/2) - c/2

where

Further epidemiological implications

• If hog population density K (as well 12)

is sufficiently high, then

HVS can coexist with, or even outcompete LVS

decreasing population density by culling migh

increase the chance of LVS to outcompete HVS

Epidemiology of classical swine fever in wild boars of Eastern Sardinia LVS

HVS

from a field survey by Guberti (1998)and Artois et al. (2002)

Parameters Symbol Value Unit

Hog carrying capacity K 600 hosts over 220 km2

Pop. growth rate r 0.5 Years-1

Natural Mortality 0.2 Years-1

Disease induced mortality

1 5 Years-1

Transmission rate 1 0.04 [# infected 1] -1 y-1

Reproductive rate Ro1 4.6

Disease induced mortality

2 15 Years-1

Transmission rate 2 0.06 [#infected 2] -1 y-1

Reproductive rate Ro2 2.37

Superinfection coeffi cient

12 0.84 [#infected 1] -1 y-1

Removal rate

Prevalence at the equilibrium as a function of culling rate, when the two strains are isolated

Prevalence at equilibrium as a function of harvesting effort for two competing strains

Number of infected individuals

The SI2R model(Susceptible-Infected-Recovered)

S

I2

I1

LVS(small1)

HVS(large 2)R

c

cc

c

Conclusions• It is possible that the reduction of host density by culling

may indeed foster the selection of less virulent strains • This in turn would reduce the threshold host density for

disease eradication• If this happens, the harvesting effort required to completely

eradicate the disease will be higher than initially expected• If culling effort is not large enough, the net effect of this

policy is to increase both prevalence and the number of infected hosts

• The harvesting effort required for the eradication of the least virulent strains may be unrealistically high (or too costly)

Further developments

• Analyse pop.dynamics by using a stochastic (possibly spatially explicit, seasonal) version of the model

• Introduce age structure and age-depedent epidemiological parameters

Su

scep

tib

les (

S)

(over 2

20

km2 )

0

100

200

300

400

time [month]

0 20 40 60 80 100

In

fecte

d (

I)

0

25

50

75

100

S

I1I2

time [month]

0 5 10 15 20

0 5 10 15 20

In

fecte

d (

I)

0.1

1

10

100

I1

I2

(LVS)

(LVS)

(HVS)

(HVS)