EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team

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EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
EPITAG – EPIdemiological modelling and control
           for Tropical AGriculture
            Inria associate team & LIRIMA team
                         2017–2019

      Suzanne TOUZEAU                      Samuel B OWONG
  BIOCORE, Inria Sophia Antipolis   University of Douala, Cameroon
    ISA, INRA Sophia Antipolis

                            January 2020

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EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
LIRIMA
= International Laboratory for Computer Sciences and Applied Mathematics
  I Before: CARI (1992–), Sarima (2004–2008)
 I 2009–2014: 12 project-teams
 I 2015–2019: Inria International Lab “LIRIMA”
     via Inria associate team programme
More: https://lirima.inria.fr/

Inria associate team
 I Aim: “fostering collaborations between Inria project teams and
   top-level research teams across the world”
 I Lifespan: 3 to 6 years
 I Exchanges of researchers and students (6 13 ke/year)
More: https://www.inria.fr/...

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EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
Where we are

               3 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
Who we are

BIOCORE                           Cameroon
  • Suzanne TOUZEAU (INRA)         •   Samuel B OWONG (Douala)
                                   •   Jean-Jules T EWA (Yaoundé 1)
  • Jean-Luc G OUZÉ
                                   •   Berge T SANOU (Dschang)
  • Frédéric G ROGNARD
                                   •   Émile M INYAKA (Douala)
  • Ludovic M AILLERET (INRA)
                                   •   Myriam D JOUKWE TAPI
  • Samuel N ILUSMAS                   (Douala, PhD 2015–)
     (INRA, PhD 2016–)             • Israël TANKAM C HEDJOU
  • Clotilde D JUIKEM                  (Yaoundé I, PhD 2016–)
     (Inria, PhD 2019–)            • Yves F OTSO F OTSO
                                       (Dschang, PhD 2017–)
                                   • Janvier P ESSER N TAHOMVUKIYE
Other participants                     (Douala, PhD 2017–)
                                   • Clotilde D JUIKEM
  I Yves D UMONT (CIRAD)
                                       (Douala, Master April 2018)
  I Gauthier S ALLET (emeritus)    • Michel M OUGANG
                                       (Douala, Master Oct. 2019)

                                                                      4 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
Context
 • Crop pests, diseases and weeds destroy up to 40% of global
   crop yields every year ⇒ threat to food security
 • Cameroon: agriculture is a major sector for employment (62%)
   and revenues (30% of exports, 15% of GDP)
 å Controlling crop pests is a major issue

Control methods
Pesticides: high financial and environmental cost, health issues
Alternatives: cropping practices, biological control, plant resistance

Why models
 I complement field studies (costly and time-consuming)
 I formalise and integrate knowledge
 I help design efficient strategies for integrated pest management

                                                                         5 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
What we do
Aims
Study the epidemiology and management of tropical crop diseases,
mathematically and numerically, with a focus on Cameroon

Approach
 I Tools from dynamical systems and control theory
 I Development and analysis of models to:
    1.   understand the plant–parasite interactions
    2.   identify relevant parameters
    3.   predict the evolution of damages
    4.   provide efficient and sustainable control strategies to limit damages

Challenges
 I Relevance of our models
    ⇒ collaboration with field experts and involvement of stakeholders
 I “Small data” in epidemiology (scarce and often qualitatively known)
                                                                             6 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
How we collaborate
              Joint PhD supervision on specific topics
              Long visits in France: 3 students/year, 3–5 months/visit

         T1. Cocoa plant mirids
         Myriam D JOUKWE TAPI, Douala–Cirad (2015–)
         S. B OWONG, L. B AGNY-B EILHE, Y. D UMONT

         T2. Plantain plant-parasitic nematodes
         Israël TANKAM C HEDJOU, Yaoundé I–Inria (2016–)
         J.-J. T EWA, L. M AILLERET, F. G ROGNARD, S. TOUZEAU

         T3. Coffee berry borers
         Yves F OTSO F OTSO, Dschang–Inria (2017–)
         B. T SANOU, S. B OWONG, F. G ROGNARD, S. TOUZEAU

         T4. Coffee leaf rust
         Clotilde D JUIKEM, MSc (2018) & PhD Inria–Douala (2019–)
         S. B OWONG, F. G ROGNARD, S. TOUZEAU
                                                                         7 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
Other research topics
Cabbage diamondback moth
  I Michel M OUGANG, MSc Douala (Oct. 2019)
    S. B OWONG
  I Aurélien Vanes K AMBEU YOUMBI, PhD Dschang (2019–)
    B. T SANOU

Maize stalk borer
  I Janvier Pesser N TAHOMVUKIYE, PhD Douala (2017–)
    S. B OWONG

Root-knot nematodes in horticultural crops
  I Samuel N ILUSMAS, PhD INRA (2016–)
    S. TOUZEAU, C. C APORALINO, V. C ALCAGNO, L. M AILLERET

                                                              8 / 46
EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
Support
 Inria associate team + UMMISCO & CIRAD

Grants
 Research schools
 I École de Contrôle Optimal Numérique, France, 2018 [Yves]
 I International Graduate School on Control, Italy, 2019 [Yves, Clotilde]
 Conferences
 I CARI, Stellenbosch, South Africa, 2018 [Israël, Yves]
 I BIOMATH , Bȩdlewo, Poland, 2019 [Israël, Yves, Clotilde]
 Mobility
 I EMS-Simons for Africa PhD development grant, 2018 [Israël]
 I AUF, Collège doctoral régional de l’Afrique Centrale et des Grands Lacs
    « Mathématiques, Informatique, Biosciences et Géosciences de
    l’Environnement », 2019 [Yves]
 PhD
 I SCAC grant, 2017 [Janvier]
 I Inria CORDI grant, 2019 [Clotilde]

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EPITAG - EPIdemiological modelling and control - for Tropical AGriculture Inria associate team & LIRIMA team
SWOT
                        Positive                        Negative

            Strengths                      Weaknesses
 Internal

            • High socio-economic impact   • Unbalanced exchanges
                                             (academic age structure)
            • Motivated students,
              jointly supervised           • Still limited scientific production
                                             (young team), fast improving
            • Involvement of CIRAD

            Opportunities                  Threats
            • Links with field partners    • Administrative hindrances
                                             for Cameroonian students
 External

            • Financial support by
              UMMISCO                      • Difficulties to ensure (other)
                                             long-lasting fundings
            • Links with INRA
                                           • Associate Team format for
                                             partners such as CIRAD

                                                                               10 / 46
Focus
        T1. Cocoa plant mirids
        Myriam D JOUKWE TAPI, Douala–Cirad (2015–)
        S. B OWONG, L. B AGNY-B EILHE, Y. D UMONT

        T2. Plantain plant-parasitic nematodes
        Israël TANKAM C HEDJOU, Yaoundé I–Inria (2016–)
        J.-J. T EWA, L. M AILLERET, F. G ROGNARD, S. TOUZEAU

        T3. Coffee berry borers
        Yves F OTSO F OTSO, Dschang–Inria (2017–)
        B. T SANOU, S. B OWONG, F. G ROGNARD, S. TOUZEAU

        T4. Coffee leaf rust
        Clotilde D JUIKEM, MSc (2018) & PhD Inria–Douala (2019–)
        S. B OWONG, F. G ROGNARD, S. TOUZEAU

                                                               11 / 46
Plantain plant-parasitic nematodes
Rosendahl

                                                                                                        D. Coyne
            A: [Jesus, Agron Sustain Dev 2014]; B: M. MacClure, Univ. Arizona; C: [Zhang, EJPP 2012]

• Major staple food – Cameroon: 2% GDP
• Nematodes (Radopholus similis): root lesions Ô great damages
  Most important pest on fruit crops in the tropics
• Control: nematicides ↔ cropping practices (soil sanitation),
  tolerant or resistant banana varieties, biological control

– Complex interaction model for the West Indies [Tixier et al. 2006]
– Partners: CIRAD and CARBAP
                                                                                                       12 / 46
Burrowing nematode (Radopholus similis) disease cycle

                                                  [F.E. Brooks 2008]
  I Obligate migratory endoparasite, < 1 mm
  I Life cycle: 20–25 days
  I Sexual reproduction & hermaphrodism (mature males not
    infective)
                                                                       13 / 46
Plant growth

   New sucker                 flowering      harvest New sucker

                root growth        fruit growth   fallow

  I Herbaceaous flowering plant, ca. 5 m
  I Single inflorescence that dies after fruiting → bunch 30–50 kg
  I Cycle: ca. 11 months, 7 months until flowering
  I Asexual reproduction by offshoots / new sucker

                                                                     14 / 46
Plant root – nematode interactions

    New sucker                 flowering      harvest New sucker

                 root growth        fruit growth   fallow

 R. similis destroy roots and affect:
  I uptake of water and nutrients Ô reduced growth & bunch weight
  I anchorage Ô toppling

                                              åDoubly hybrid system

                                                                  15 / 46
Model: initialisation
                             New sucker             flowering     harvest       New sucker

                                      root growth          fruit growth       fallow
                              0                        d                  D     τ      T

                S
                X

      P
                        
                        
                         S(0) = S0       plant root
                        
                        
                        
                          P(0) = P0       nematodes
                                            in soil
                        
                        
                        
                        
                        X (0) = 0        nematodes
                                            in root

 Hypothesis: nematode-free sucker

                                                                                           16 / 46
Model: cropping season
                                    New sucker             flowering        harvest       New sucker

                                           root growth               fruit growth       fallow
                                     0                           d                  D     τ      T
                                          ρ(t)=ρ                      ρ(t)=0

 ρ(1-X/K)              S
                              δX/(S+Δ)
                       X
             βS    μ          αδX/(S+Δ)
  ω                      γ                          plant root       nematodes

         P             1-γ
               root growth                  root consumption
      
            z       }|      {                 z }| {
      
      
      
                           S                       SX
      
       Ṡ = ρ(t) S 1 −                        −δ
      
                          K                        S+∆
      
      
                                                     SX
        Ṗ =                   − βPS + δ                    α (1 − γ)                   − ωP
      
                                                   S+∆
      
      
      
                                                    SX
      
      Ẋ =                     +βP S +δ                    αγ                          −µX
      
                               | {z }             S+∆                                  | {z }
      
                              root entering
                                              |         {z          }               mortality
                                                 feeding & reproduction

                                                                                                     17 / 46
Model: harvest
                         New sucker           flowering     harvest       New sucker

                                root growth          fruit growth       fallow
                         0                       d                  D     τ      T

             S
             X

     P
            
            
             S(D + ) = 0                     plant root
            
            
            
              P(D + ) = P(D) + q X (D)        nematodes
                                                in soil
            
            
            
            
            X (D + ) = 0                     nematodes
                                                in root

                                                                                     18 / 46
Model: fallow
                          New sucker            flowering      harvest       New sucker

                                  root growth           fruit growth       fallow
                          0                         d                  D     τ      T

                S
                X
  ω
      P
                    
                    
                     Ṡ = 0           plant root
                    
                    
                      Ṗ = −ω P        nematodes
                                         in soil
                    
                    
                    
                    Ẋ = 0            nematodes
                                         in root

                                        
                ⇒ P(T ) = P(D) + q X (D) e−ω τ

                                                                                        19 / 46
Model: new sucker
                              New sucker           flowering       harvest       New sucker

                                     root growth            fruit growth       fallow
                               0                        d                  D     τ      T

                 S
                 X

       P
                      
                      
                       S(T + ) = S0       plant root
                      
                      
                      
                        P(T + ) = P(T )    nematodes
                                             in soil
                      
                      
                      
                      
                      X (T + ) = 0        nematodes
                                             in root

 Etc. for the next periods, with transition law:
                                                 
             P(Tk +1 ) = P(Tk + D) + q X (Tk + D) e−ω τ

                                                                                            20 / 46
Analysis

  I Model reduction and analysis (fast root infections)
      I Local stability results for the pest-free equilibrium
      I Exact solutions for the linearised model
  I Conditions for pest extinction, depending on fallow duration (τ )

             I. Tankam, S. Touzeau, F. Grognard, L. Mailleret, J.-J. Tewa, 2018.
             A multi-seasonal model of the dynamics of banana plant-parasitic
             nematodes.

     I. Tankam, S. Touzeau, L. Mailleret, J.-J. Tewa, F. Grognard, 2019. Modelling
     and control of a banana soilborne pest in a multi-seasonal framework.
     Mathematical Biosciences. In revision.

                                                                                   21 / 46
Optimisation

   I Aim: maximise the cumulated yield, while minimising the costs
     (new suckers), on a fixed multi-seasonal time horizon (Tmax )
   I Control: fallow period durations (τk )

 New sucker           flowering        harvest            New sucker   flowering       harvest

        root growth          fruit growth       fallow
 0                       d                  D    τ1 T1                T1+d       T1+D τ2 T2         Tmax
          W(t)=0                  w                              0               w         0

     • fixed cropping period D & fixed delay before flowering d
     • fixed cost of a new pest-free sucker c
                            R T +D              R T +D
     • seasonal yield Yk = Tkk W (t) S(t) dt = w Tkk+d S(t) dt
       seasonal profit Rk = Yk − c

                                                                                       Pn
      Maximise profit: maxτ =(τ1 ,...,τn ) R(τ ) with R(τ ) =                             k =0 Rk

                                                                                                      22 / 46
Variable fallow durations
       D          τ1         D       τ2       D         τ3        D
       1                      2                3                   4
0                      T1               T2                   T3          Tmax

 Solutions
 • τk ∈ [0, Tmax − 2 D] → at least 2 cropping seasons
 • Pests “not too abundant”
 Admissible fallows τ = (τ1 , . . . , τn ) such that last season ends at Tmax
        n + 1 complete cropping seasons
    →
        n fallows

 Procedure
    1. Solve the optimisation problem for n = 1, . . . , nmax
                                  Pn
         • over the n-simplex : k =1 τk = Tmax − (n + 1)D
         • Adaptive Random Search algorithm
    2. Select the highest profit among the nmax optima

                                                                                23 / 46
Numerical application

  Parameter value unit                                      Parameter                value unit
   banana roots                                              nematode
      d         210 days 1                                      δ                 2.10−4         g.day−1
      D         330 days 1                                      ∆                     60         g
      ρ       0.025 day−1                                       α                    400         g−1
      K         150 g 2                                         γ                     0.5
      S0         60 g 2                                         β                   10−1         g−1 .day−1
   banana production                                            µ                  0.045         day−1 3
      w          0.3 CFA.g−1 .day−1                             ω                 0.0495         day−1 4
   simulation                                                   P0                   100
     Tmax     4000 days                                      harvest
   1
       [Banana cultivation guide, 2018] 2 [Serrano, 2005]       q                       5%
                                                             3
                                                                 [Sarah et al., 1996] 4 [Chabrier et al., 2008]

                                                                                                                  24 / 46
Result

å Maximum profit: 54,600 CFA for variable fallows over 11 seasons
 (nmax = 12 cropping seasons)

                                                               25 / 46
Regulations                                                   distance to
                                                            simplex centre
                                                       z }| {
Bounded fallow: τsup = 60 days     Penalty: R̄ = R − r d(τ, τ0 )
                                                   R(τ0 )
                                       with r =   10×dmax
                                       (penalty < “regular” profit / 10)

å Maximum profit: 54,400 CFA       å Maximum profit: 53,500 CFA
 over 11 seasons                    over 11 seasons

               Still 11 cropping seasons
               Almost no profit loss with regulations

                                                                             26 / 46
Constant fallow duration

      D       τ        D        τ        D       τ          D
      1                2                 3                  4
0                 T                 2T               3T         Tmax

 Solutions
 Solution(s) of the optimisation problem in discrete set:
                                                
                                    Tmax − D
                      Ξ= τ >0:                ∈N
                                      D+τ

 Procedure
 Exhaustive exploration

                                                                       27 / 46
Result
                 12          11   10   9 8 7 6 5 4   3   2
  profit (CFA)

                           τ (days)

å Maximum profit: 52,000 CFA over 11 cropping seasons
 for τ = 37 days ∈ Ξ
                                                             28 / 46
Comparisons

              Similar profits

              High final soil infestations
              with variable fallows

                                        29 / 46
Conclusions
  I Banana – nematode interaction model, with pest-free suckers
    planted at each cropping season
  I Optimal fallow durations: best profit with non constant fallows
    (even when regulated), but minor gains and high final soil
    infestations

                            I. Tankam, S. Touzeau, F. Grognard, L. Mailleret, J.-
                            J. Tewa, 2018. An agricultural control of Radopholus
                            similis in banana plantations

                            I. Tankam, S. Touzeau, F. Grognard, L. Mailleret, J.-J.
                            Tewa, 2019. Agricultural control of Radopholus similis
                            in banana and plantain plantations

     I. Tankam, F. Grognard, L. Mailleret, J.-J. Tewa, S. Touzeau, 2019. Optimal and
     sustainable management of a soilborne banana pest. In prep.

                                                                                 30 / 46
Focus
        T1. Cocoa plant mirids
        Myriam D JOUKWE TAPI, Douala–Cirad (2015–)
        S. B OWONG, L. B AGNY-B EILHE, Y. D UMONT

        T2. Plantain plant-parasitic nematodes
        Israël TANKAM C HEDJOU, Yaoundé I–Inria (2016–)
        J.-J. T EWA, L. M AILLERET, F. G ROGNARD, S. TOUZEAU

        T3. Coffee berry borers
        Yves F OTSO F OTSO, Dschang–Inria (2017–)
        B. T SANOU, S. B OWONG, F. G ROGNARD, S. TOUZEAU

        T4. Coffee leaf rust
        Clotilde D JUIKEM, MSc (2018) & PhD Inria–Douala (2019–)
        S. B OWONG, F. G ROGNARD, S. TOUZEAU

                                                               31 / 46
Coffee berry borers (CBB)

                                                                     [Burbano, JIS 2011]
                  Uccao Cameroun

I Coffee is an important cash crop in the tropics
I Borers (Hypothenemus hampei) mostly develop and feed in coffee
  berries, inducing great damages
     • reduction in berry quality and yield
     • economic losses > 500 million $/year

I Simulation model with crop growth and pest control [Gutierrez et al.
   1998; Rodríguez et al. 2011; Rodríguez et al. 2013]

                                                                    32 / 46
CBB life cycle
 I   Microscopic beetle < 1.5 mm
 I   Life cycle ca. 4 weeks
 I   1–3 eggs/day during ca. 20 days
 I   Sex ratio 10 ~ / 1 |

                                       33 / 46
CBB life cycle

 I ~ bore into a berry
 I Mating occurs inside the berry
 I Fertilised ~ fly out to infest new berries
 I | stay in berry

                                                [Bustillo et al. 1998]
                                                                         34 / 46
Variables

                         s
                                             z i
                         y

Single season model
  I s(t): healthy coffee berries
  I i(t): infested coffee berries
  I y (t): colonizing females (outside the berries)
  I z(t): infesting females (inside the berries)
Hypothesis: males are not limiting

                                                      35 / 46
Model
                                      μ
                    Λ                            β                   μi
                             s                  y+αs
                                                             z i
                                            ε
                             y                                  μz
                                                φ
                                 μy

        
                                     infestation
        
              new berries
                                        sy          mortality
        
         ṡ =     Λ             −β                 −µs
        
        
        
                                    y + αs
        
                                       sy
        
         i̇ = Λ                 + β               − µi i       infected berries
                                      y + αs
        
             emergence
        
                                       sy
        
        ẏ =    ϕz              − εβ               − µy y
        
                                     y + αs
        
        
        
                                       sy
        ż = ϕz                 + εβ               − µz z
                                      y + αs

                                                                                    36 / 46
Stability of the equilibria
                                              
                                    Λ
 Pest-free equilibrium (PFE)        µ , 0, 0
  I LAS → Basic reproduction number (next-generation matrix):

                                          εβϕ α1
                            N =                        1

                                                                               37 / 46
CBB control
I Insecticides

I Cropping practices:
  removing dropped berries,
  strip-picking, stump pruning

I Trapping

                                                       Brocap
                                                       R
I Biological control
  • Parasitoid (Phymastichus coffea) or predator (Cathartus quadricollis)
    insects
                             A. Castillo, F. Infante

                                                                              [Follett et al., 2016]
                                                                A. Ramirez

  • Entomopathogenic fungi (Beauveria bassiana)
                                                                             38 / 46
Model with control
                                           sy
               
                ṡ = Λ − (1 − σ(v ))    β       − µs
               
                                         y + αs
               
               
               
                                           sy
               ẏ = ϕz−               εβ        − µy y
                                          y + αs
               
                                           sy
               
                ż   =   +(1 − σ(v )) εβ        − µz z
               
                                         y + αs
               
               
               
                v̇    = −γv + h(t)
  I Fungus load v (t) reduces the infection of healthy berries
    with a saturation effect:
                           ξv
              σ(v ) =            with maximum efficacy ξ 6 1
                         v +k
  I Fungus load v (t) persists in the plantation
    → control h(t) ∈ [0, hmax ]

                                                                 39 / 46
Optimal control

 Maximise the yield at the end of the cropping season s(tf ),
 while minimising the control costs (↔ maximise profit)
 & the CBB population for the next cropping season y (tf ):
                                     Z   tf
               J (h) = ζs s(tf ) −            C hθ (t) dt − ζy y (tf )
                                     0
                         yield                 costs         CBB pop.

               with linear (θ = 1) or quadratic (θ = 2) costs

 → Pontryagin’s Maximum Principle for quadratic cost (θ = 2):
                                         
         ∗                   p4 (t)
        h (t) = max 0, min −        , hmax      h∗ (tf ) = 0
                              2C

 → PMP for linear cost (θ = 1):
   bang-bang & singular control
                                                                         40 / 46
Table 1
Numerical        application: linear cost
       Biological meaning and value of parameters (with s in number of berries, y and z in number of
   females and v in gram).

         Parameter     Biological meaning                                    Value
         Λ             Production rate of new coffee berries                 1200 berries.day−1
         µ             Natural mortality rate of healthy coffee berries      0.002 day−1
         φ             Emergence of new colonizing females                   2 day−1
         β             Infestation rate                                      0.01 day−1
         ε             Conversion rate from coffee berries to CBB            1 female berry−1
         µy            Natural mortality rate of colonizing females          1/20 day−1
         µz            Natural mortality rate of infesting females           1/27 day−1
         ξ             Maximum effectiveness rate of fungus                  0.8
         α             The interference amplitude                            0.7
         k             Maximal amount the fungus                             200 g.day−1
         γ             Rate of fungus decay                                  1/50 day−1
         ζs            Weight of coffee berries                              2.10−3 $.day −1
         ζy            Weight of colonizing female                           10−4 $.f emale−1
         C             Cost per unit of fungus                               0.022$.g −1 .day
         hM            Maximal amount fungus to apply                        30g.day −1

  427     6. Conclusion. In this paper, we have developed a basic model to study the
  Numerical
  428 infestation method
                  dynamic of coffee berries by CBB inside the plantation.   This model is
  429 based on the CBB life cycle and take into account the availability of healthy coffee
  BOCOP
  430 berries.direct methodanalysis show that the dynamic of CBB varies according
                Our theoretical

                                                                                                       41 / 46
low initial infestation y0 = 104 ~
                       ×10   5        (a) Healthy coffee berries                                          ×10 5        (b) Colonizing females
                  3                                                                                 15

                                                                                      y [females]
                                                                                                     y*
    s [berries]

                  2                                                                                 10

                  s*
                  1                                                                                  5

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                       ×10 4            (c) Infesting females                                                              (d) Fungus load
                  4                                                                      1500
    z [females]

                  z*                                                                     1000

                                                                              v [g]
                  2
                                                                                               500

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                                       (e) Fungus application                                                          (f) Effect of fungus load
             30                                                                                      1
h [g/day]

             20
                                                                                      σ(v)

                                                                                                    0.5
             10

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                                                                                                                                                         42 / 46
high initial infestation y0 = 106 ~
                       ×10   5        (a) Healthy coffee berries                                          ×10 5        (b) Colonizing females
                  4                                                                                 15

                                                                                      y [females]
    s [berries]

                                                                                                     y*
                                                                                                    10
                  2
                  s*                                                                                 5

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                       ×10 4            (c) Infesting females                                                              (d) Fungus load
                  3                                                                      2000
                  z*
    z [females]

                  2

                                                                              v [g]
                                                                                         1000
                  1

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                                       (e) Fungus application                                                          (f) Effect of fungus load
             30                                                                                      1
h [g/day]

             20
                                                                                      σ(v)

                                                                                                    0.5
             10

                  0                                                                                  0
                      0          50         100      150        200   250                                 0       50        100       150          200   250
                                            Time (days)                                                                      Time (days)

                                                                                                                                                         43 / 46
Conclusions
  I CBB-berry interaction model, for a single cropping season
  I Entomopathogenic fungi can limit the CBB infestation
  I Optimal control on a simple model gives a rough idea of how
    pest control should be applied

          Y. Fotso Fotso, F. Grognard, B. Tsanou,
          S. Touzeau, 2018. Modelling and control
          of coffee berry borer infestation

                                 Y. Fotso, F. Grognard, S. Touzeau, B. Tsanou,
                                 S. Bowong, 2019. Optimal control on a simple
                                 model of coffee berry borer infestation

     Y. Fotso, F. Grognard, S. Touzeau, B. Tsanou, S. Bowong, 2019. Modelling and
     optimal strategy to control coffee berry borer infestation. In prep.

                                                                               44 / 46
What next

PhD defenses
4 students will very soon defend their thesis (early 2020):
  I Myriam D JOUKWE TAPI
  I Samuel N ILUSMAS
  I Janvier P ESSER N TAHOMVUKIYE
  I Israël TANKAM C HEDJOU

EPITAG = fairly young team, based on joint PhD supervisions
 I Associate team renewed for 3 more years, with similar overall
    objectives
 I Pursue the research topics and associated PhD theses
    (finishing, ongoing, starting)

                                                                   45 / 46
In short

                      French & Cameroonian researchers and students

 with a background in dynamical systems
 and control

                                          and an interest in crop diseases
           D. Coyne

            More on EPITAG: https://team.inria.fr/epitag/

                                                                         46 / 46
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