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A model for the operations to render epidemic-free a hog farm infected by the Aujeszky disease

A. Costamagna
A. Costamagna
, 
M. Drigo
M. Drigo
, 
M. Martini
M. Martini
, 
B. Sona
B. Sona
 and 
E. Venturino
E. Venturino
   | Mar 15, 2016
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Published Online: Mar 15, 2016
Page range: 207 - 228
Received: Dec 23, 2015
Accepted: Mar 13, 2016
DOI: https://doi.org/10.21042/AMNS.2016.1.00016
Keywords
© 2016 A. Costamagna, M. Drigo, M. Martini, B. Sona, E. Venturino published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Gestation room with individual boxes.
Gestation room with individual boxes.

Fig. 2

Weaning unit.
Weaning unit.

Fig. 3

Fattening unit, with several animals in each box.
Fattening unit, with several animals in each box.

Fig. 4

Infected weaned pigs evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.
Infected weaned pigs evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.

Fig. 5

Infected sows evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.
Infected sows evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.

Fig. 6

Percentage of infected sows evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.
Percentage of infected sows evolution during a whole year. Here we fix the value of external contamination rate at τ = 0.003.

Fig. 7

Infected weaned pigs evolution during a whole year. Here we fix the value of biohazard rate at Δ = 0.002.
Infected weaned pigs evolution during a whole year. Here we fix the value of biohazard rate at Δ = 0.002.

Fig. 8

Infected sows evolution during a whole year. Here we fix the value of biohazard rate at Δ = 0.002.
Infected sows evolution during a whole year. Here we fix the value of biohazard rate at Δ = 0.002.

Fig. 9

Percentage of infected sows evolution during a whole year. Here we fix the value of biohazard rate at D = 0.002.
Percentage of infected sows evolution during a whole year. Here we fix the value of biohazard rate at D = 0.002.

Fig. 10

Reference values in the fattening unit for no external contamination rate and biohazards, τ = 0, Δ = 0, with an average value of 35.48%.
Reference values in the fattening unit for no external contamination rate and biohazards, τ = 0, Δ = 0, with an average value of 35.48%.

Fig. 11

Left: Percentage of infected pigs evolution in the fattening unit. Here we fix the value of external contamination rate at τ = 0.003. Right: Averages in time as function of Δ of the percentage of infected pigs evolution in the fattening unit. Here we fix the value of external contamination rate at τ = 0.003.
Left: Percentage of infected pigs evolution in the fattening unit. Here we fix the value of external contamination rate at τ = 0.003. Right: Averages in time as function of Δ of the percentage of infected pigs evolution in the fattening unit. Here we fix the value of external contamination rate at τ = 0.003.

Fig. 12

Left: Percentage of infected pigs evolution in the fattening unit. Here we fix the value of biohazard rate at Δ = 0.002. Right: Averages in time as function of τ of the percentage of infected pigs evolution in the fattening unit. Here we fix the value of biohazard rate at Δ = 0.002.
Left: Percentage of infected pigs evolution in the fattening unit. Here we fix the value of biohazard rate at Δ = 0.002. Right: Averages in time as function of τ of the percentage of infected pigs evolution in the fattening unit. Here we fix the value of biohazard rate at Δ = 0.002.

Fig. 13

Reference values in case of bad implementation of the vaccine for no external contamination rate and biohazards, τ = 0, Δ = 0, with an average value of 35.48%.
Reference values in case of bad implementation of the vaccine for no external contamination rate and biohazards, τ = 0, Δ = 0, with an average value of 35.48%.

Fig. 14

Top. Left: Percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of external contamination rate at τ = 0.003. Right: The same figure for new infected pigs. Bottom. Averages in time as function of Δ of the percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of external contamination rate at τ = 0.003.
Top. Left: Percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of external contamination rate at τ = 0.003. Right: The same figure for new infected pigs. Bottom. Averages in time as function of Δ of the percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of external contamination rate at τ = 0.003.

Fig. 15

Top. Left: Percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of biohazard rate at Δ = 0.002. Right: The same figure for new infected pigs. Bottom. Averages in time as function of τ of the percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of biohazard rate at Δ = 0.002.
Top. Left: Percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of biohazard rate at Δ = 0.002. Right: The same figure for new infected pigs. Bottom. Averages in time as function of τ of the percentage of infected pigs evolution in case of bad implementation of the vaccine. Here we fix the value of biohazard rate at Δ = 0.002.

Fig. 16

Sensitivity of x with respect (left to right) the parameters m, τ and α.
Sensitivity of x with respect (left to right) the parameters m, τ and α.

Fig. 17

Sensitivity of z with respect (left to right) the parameters m, Δ and β.
Sensitivity of z with respect (left to right) the parameters m, Δ and β.

Fig. 18

Sensitivity of u with respect (left to right) the parameters b, Δ and γ.
Sensitivity of u with respect (left to right) the parameters b, Δ and γ.

Fig. 19

Correlations between the system’s parameters and the infected (left), immunized (center) and susceptible (right) populations in the gestation and farrowing units. The parameters, bottom to top, are the following ones: m, α, τ, Δ, β , b, γ. In each frame, the left column contains the results relative to the sows in the gestation room, the central one the sows in the farrowing unit and the right one the newborns in the farrowing unit.
Correlations between the system’s parameters and the infected (left), immunized (center) and susceptible (right) populations in the gestation and farrowing units. The parameters, bottom to top, are the following ones: m, α, τ, Δ, β , b, γ. In each frame, the left column contains the results relative to the sows in the gestation room, the central one the sows in the farrowing unit and the right one the newborns in the farrowing unit.

Comparison between the actual and the simulated number of newborns

actual number of newborns January - April

simulation

1600

1668.1851

actual number of newborns January - August

simulation

3450

3512.6317

actual number of newborns January - December

simulation

5160

5281.3771

Simulation of monthly percentages of infected sows

JanFebMarchApril
infected sows60.963970.025779.291684.6477
percentage of infected sows19.6522.7025.7727.85
MayJuneJulyAug
infected sows85.758873.341675.588477.6100
percentage of infected sows26.8726.1525.1326.4000
SeptOctNovDec
infected sows77.559577.489677.101175.1609
percentage of infected sows25.6624.9624.9722.78

Comparison between the actual and the simulated number of sows

actual number of sows: January - April

simulation

1251

1230.40

actual number of sows: January - August

simulation

2446

2424.85

actual number of sows : January - December

simulation

3652

3676.35

j.AMNS.2016.1.00016.untab.001.w2aab3b7e1276b1b6b1ab1b5b4c11aAa

simulationτ = 0.003# infected weaned pigsaverage % infected sows
Reference: ∆ = 0, τ = 02.24414.44
C: Δ = 02.366723.86
H: Δ = 0.001101.604228.15
A: Δ = 0.00228.32424.91
F: Δ = 0.00339.94725.39
G: Δ = 0.00670.176826.69
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