Post on 02-Jun-2020
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Whitefly-transmitted Tomato Severe RugoseVirus
IV Southern-Summer School on Mathematical Biology
ICTP-SAIFR
22 January 2017
1 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Outline
1 Group Work
2 The problem
3 Transmission Process
4 Life Cycle of Bemisia tabaci
5 AssignmentModel Assumptions
6 The ModelDefinition of the parametersFixed Points
7 Results
8 Conclusion
2 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Group work
Rodrigo Corder
USP-Brasil Pablo Pesco
UBA - Argen�na Alicia RamirezUNICAMP-Brasil
José Bruno Malaquias
ESALQ-USP-Brasil
Alan Barzilay
USP-Brasil
Hendrik Sulbaran
IVIC-Venezuela
3 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
The problem
4 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Transmission Process
5 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Life cycle of Bemisia tabaci
6 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Assignment
To develop a mathematical model combining epidemiologicaland ecological dynamics that describe the interaction betweenwhiteflies, tomatoes and the disease. Use it to understand theecological and epidemiological consequences of TSRV[1].
Questions
Is ”vazio sanitario” e�cient in order to reduce the incidence ofTSRV?
7 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Model Assumptions
1 Number of tomatos plants constants: (Sp + Ip = const.).
2 Virus vertical transmission between whiteflies.
3 Primary infections: whiteflies vs plants.
4 Secondary infection: plants vs plants.
5 No plants (in for not) during harvest.
6 Removal of all plants during harvest.
7 Carrying capacity for whiteflies.
8 Higher mortality rate of infected than susceptiblewhiteflies.
9 Migration.
10 Period of tomato-free-plants promotes reduction ofwhiteflies.
8 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
The Model
Interaction between susceptible plants, infected plants, suscep-tible whiteflies and infected whiteflies.
9 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Mathematical model:
dSp
dt
= �dIp
dt
; Sp + Ip = ⇣
dIp
dt
= ⇢SpIp + ↵SpIw
dSw
dt
= ��Sw Ip + rSw
✓⇣ � (Sw + Iw )
K
◆+m (1)
dIw
dt
= �Sw Ip + rSw
✓⇣ � (Iw + Iw )
K
◆� µIw +m
Ip = infected plants, Iw = infected whiteflies,
Sw = susceptible whiteflies, Sp = susceptible plants.
10 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Definition of the parameters
We have defined the following parameters for our model:
⇢ = infection rate between plants;
↵ = plant infection rate due to infected whiteflies;
� = whitefly infection rate due to infected plants;
r = intrinsic rate growth of whiteflies;
µ = increased death rate due of infection;
K = carrying capacity;
m = migration.
11 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Units:
⇢ : [⇢] =1
ind.temp, ↵ : [↵] =
1
ind.temp, � : [�] =
1
ind.temp,
r : [r ] =1
ind.temp, µ : [µ] =
1
ind.temp, K =
ind.
unit area
12 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Fixed Points
P = (S⇤p , I
⇤p , S
⇤w , I
⇤w )
P
1,2 =
1, 0,
1
2
K ±
rK
r
(Kr + 4m)
!, 0
!(2)
P3,4 =
✓0, 1,
✓rI 2w � K(r � µ)Iw � Km
�K � rIw
◆,
✓KmrSw
+1r(K(r � �)� rSw )
◆◆
(3)
13 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Results
Temporal evolution of dynamics:
14 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
4 cycles:
15 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
16 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Migration
Considering a scenario with no infected plants and no infectedwhiteflies in the beginning of the cycle.
17 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Condition: ”Vazio sanitario”.Phase-portrait:
0
50
100
150
200
-10 0 10 20 30 40 50 60 70
Infe
ctio
us W
hite
-flie
s
Susceptible White-flies
Nulcline dS=0Nulcline dI=0
Trajectory
18 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Condition: plantation.Phase-portrait:
0
100
200
300
400
500
600
700
800
0 50 100 150 200 250 300 350 400
Infe
ctio
us W
hite
-flie
s
Susceptible White-flies
Nulcline dS=0Nulcline dI=0
Trajectory
19 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Condition: plantation.Time evolution:
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000Time (days)
Susceptibles whitefliesInfected whiteflies
20 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Conclusion
1 Tomato-free plants period is e�cient in some conditions.
2 In case of high migration, it is necessary to combinetomato-free plants period with others control strategies toprevent the dissemination diseases.
3 How can the model give us insights into others agriculturalproblems?
21 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Conclusion
1 Tomato-free plants period is e�cient in some conditions.
2 In case of high migration, it is necessary to combinetomato-free plants period with others control strategies toprevent the dissemination diseases.
3 How can the model give us insights into others agriculturalproblems?
21 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Conclusion
1 Tomato-free plants period is e�cient in some conditions.
2 In case of high migration, it is necessary to combinetomato-free plants period with others control strategies toprevent the dissemination diseases.
3 How can the model give us insights into others agriculturalproblems?
21 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
Barbosa, J.C., Rezende, J.A. and Amorim, L., 2016.Temporal dynamics of Tomato severe rugose virus andBemisia tabaci in tomato fields in So Paulo, Brazil. Journalof Phytopathology, 164(1), pp.1-10.
Kliot, Adi., and Ghanim, Murad., 2013. The role ofbacterial Chaperones in Circulative Transmission of plantViruses by Insect vectors. Viruses 5, 1516-1535.doi:10.3390/v5061516
22 / 23
Whitefly-
transmitted
Tomato
Severe Rugose
Virus
Group Work
The problem
Transmission
Process
Life Cycle of
Bemisia tabaci
Assignment
Model
Assumptions
The Model
Definition of the
parameters
Fixed Points
Results
Conclusion
23 / 23