# Mathematical modeling, analysis and control of African cassava mosaic disease

Armando Borel Kenne Meli, Suzanne Touzeau, Frédéric Grognard, Jean Jules Tewa

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Armando Borel Kenne Meli, Suzanne Touzeau, Frédéric Grognard, Jean Jules Tewa. Mathematical modeling, analysis and control of African cassava mosaic disease. MPDEE 2025 - Conference on Mathematical Population Dynamics, Ecology and Evolution, May 2025, Bilbao, Spain., 2025. hal-05167011

HAL Id: hal-05167011

https://inria.hal.science/hal-05167011v1

Submitted on 17 Jul 2025

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Mathematical modeling, analysis and control of African cassava mosaic disease

Armando Borel Kenne Meli*<fnref n="1" />,<fnref n="2" />,<fnref n="3" />, Suzanne Touzeau<fnref n="1" />,<fnref n="2" />, Frédéric Grognard<fnref n="2" />,
Jean Jules Tewa<fnref n="3" />

## 1. Context

### Cassava (Manihot esculanta Crantz)

* major staple food in the tropics

* about 700 million people depend on cassava

### African cassava mosaic disease

* viral disease transmitted by the whitefly (Bemisia tabaci)

* disease affects many plant hosts

### Control

* resistant/tolerant cassava plants (with different resistance levels)

* phytosanitation, including healthy cuttings and roguing

* biological control based on natural enemies

<figure><img src="image_2.png" /></figure>

## 2. Research question

► Cassava mosaic disease control through resistance deployment and tool cleaning

## 4. Model simulation

Only susceptible plants and hosts:

$$ \kappa_c = 1, \kappa_r = 0, \alpha_{rs} = 0.3, \alpha_{cs} = 0.4 $$

<figure><img src="image_3.png" /></figure>

Some resistant plants:

$$ \kappa_c = 0.5, \kappa_r = 0.5, \alpha_{rs} = 0.3, \alpha_{cs} = 0.4 $$

<figure><img src="image_4.png" /></figure>

Some resistant plants & tool cleaning:

$$ \kappa_c = 0.5, \kappa_r = 0.5, \alpha_{rs} = 0, \alpha_{cs} = 0 $$

<figure><img src="image_5.png" /></figure>

## 3. Epidemiological model

<figure><img src="image_6.png" /></figure>

$$
\left\{
\begin{aligned}
\frac{dS_x}{dt} &= \left( r_{xs}(1-\alpha_{xs})S_x + (1-\alpha_{xi})r_{xi}I_x \right) \left( 1 - \frac{S_x + I_x}{K_x} \right) - \beta_x S_x I_v \\
\frac{dI_x}{dt} &= \left( r_{xi}\alpha_{xi}I_x + r_{xs}\alpha_{xs}S_r \right) \left( 1 - \frac{S_x + I_x}{K_x} \right) + \beta_x S_x I_v - \mu_I I_x \\
\frac{dS_v}{dt} &= r_v \left( S_v + I_v \right) \left( 1 - \frac{S_v + I_v}{K_v} \right) - \beta_{vx} S_v I_x \\
\frac{dI_v}{dt} &= \beta_{vx} S_v I_x - \mu_v I_v
\end{aligned}
\right.
$$

* 4 populations (index): susceptible (x = c) and resistant (x = r) cassava, alternative hosts (x = h) and vectors (v)

* 2 states per population: S<sub>x</sub> healthy and I<sub>x</sub> infected

► 8 state variables

## 5. Results & perspectives

### Simplified model: resistant cassava and vectors only

* disease-free equilibrium ($\kappa_r, 0, \kappa_v, 0$) asymptotically stable iff $\alpha_{rs} < \frac{1}{2}$

### Simulations of the full model

* resistance improves yield but does not protect susceptible plants

* tool cleaning results in more healthy resistant plants

### Perspectives

* optimal resistance deployment, taking increased cost of seeds into account

* development of a seasonal epidemiological model

<footnote n="1">¹Université Côte d'Azur, INRAE, ISA, France</footnote>

<footnote n="2">²Université Côte d'Azur, Inria, INRAE, CNRS, MACBES, France</footnote>

<footnote n="3">³University of Yaoundé I, ENSPY, UMI 209 UMMISCO, Cameroon</footnote>