An optimal control model for Coffee Berry Disease and Coffee Leaf Rust co-infection


  • Halson Nyaberi Kenyatta University
  • W.N. MUTUKU Department of Mathematics, Kenyatta University, Kenya
  • D.M. MALONZA Department of Mathematics, South Eastern University of Kenya
  • G.W. GACHIGUA Department of Industrial and Engineering Mathematics, The Technical University of Kenya
  • G.O. ALWORAH Department of Plant Pathology, KALRO-Coffee Research Institute, Kenya


Coffee Berry Disease, Coffee Leaf Rust, Optimal control, Numerical Simulation


In the 1980s, coffee production in Kenya peaked at an average of 1.7 million bags annually. Since then,
this production has declined to the current output of below 0.9 million bags annually. Coffee berry disease
(CBD) and Coffee leaf rust (CLR) are some of the causes of this decline. This is due to insufficient knowledge
of optimal control strategies for CBD and CLR co-infection. In this research, we derive a system of ODEs from
the mathematical model for co-infection of CBD and CLR with control strategies to perform optimal control
analysis. An optimal control problem is formulated and solved using Pontryagin’s maximum principle. The
outcomes of the model’s numerical simulations indicate that combining all interventions is the best strategy
for slowing the spread of the CBD-CLR co-infection.


Download data is not yet available.


Coffee production in Kenya. Retrieved May 13, 2021, from

K. Condliffe, W. Kebuchi, C. Love, and R. Ruparell, “Kenya coffee: a cluster analysis” Professor Michael Porter, Microeconomics of Competitiveness. Harvard Business

School, 2, 2008

J. McDonald, “A preliminary account of a disease of green coffee berries in Kenya,”

Transactions of the British Mycological Society. 11 (1–2): 145–154,1926. doi :


E. K. Gichuru, J. M. Ithiru, M. C. Silva, A. P. Pereira, and V. M. Varzea, “Additional physiological races of coffee leaf rust (Hemileia vastatrix) identified in Kenya,”

Tropical Plant Pathology, 37(6), 424-427, 2012.

R. W. Rayner, “Rust disease of coffee,” World Crops 12:222-224,1960.

H. O. Nyaberi, W. N. Mutuku, D. M. Malonza, and G. W. Gachigua, “ A Mathematical Model of the Dynamics of Coffee Berry Disease,” Journal of Applied Mathematics,

B. Nannyonga, L. Luboobi, P. Tushemerirwe, and M. Jab lo´nska-Sabuka, “Using contaminated tools fuels outbreaks of Banana Xanthomonas Wilt: An optimal control

study within-plantations using Runge-Kutta 4th order algorithms,” International

Journal of Biomathematics, 8(05), 1550065,2015.

G. Alworah and E. Gichuru, “ Advances in the Management of Coffee Berry Disease

and Coffee Leaf Rust in Kenya,” Journal of Renewable Agriculture 2(1):5, 2014. DOI:


J. Avelino, H. Zelaya, A. Merlo, A. Pineda, M. Ord´o˜nez, and S. Savary, “The intensity

of a coffee rust epidemic is dependent on production situations,” Ecological modelling,

(3-4), 431-447, 2006.

J. Vandermeer and P. Rohani, “The interaction of regional and local in the dynamics

of the coffee rust disease,” arXiv preprint arXiv:1407.8247, 2014.

J. Vandermeer, Z. Hajian-Forooshani, and I. Perfecto, “The dynamics of the coffee

rust disease: an epidemiological approach using network theory” European journal

of plant pathology, 150(4), 1001-1010, 2018.

C. Djuikem, F. Grognard, R. T. Wafo, S. Touzeau, and S. Bowong,“Modelling coffee leaf rust dynamics to control its spread,” Mathematical Modelling of Natural

Phenomena, 16, 26, 2021.

C. Djuikem, A. G. Yabo, F. Grognard, and S. Touzeau, “ Mathematical modelling and

optimal control of the seasonal coffee leaf rust propagation,” IFAC-PapersOnLine,

(5), 193-198, 2021.

L. I. Roeger, Z. Feng, and C. Castillo-Chavez, “Modeling TB and HIV coinfections,” Mathematical biosciences and engineering : MBE, 6(4), 815–837, 2009.

J. K. Nthiiri, G. O. Lawi, and A. Manyonge, “Mathematical modelling of tuberculosis as an opportunistic respiratory co-infection in HIV / AIDS in the presence of

protection,” Appl. Math. Sci. 9(105): 5215–5233, 2015.

K. O. Okosun, and O. D. Makinde, “A co-infection model of malaria and cholera

diseases with optimal control’” Mathematical Biosciences, 258, 19-32, ISSN 0025-

, 2014.

T. T. Getachew, D. M. Oluwole and D. Malonza, “Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis,” Applied Mathematics and Computation, 316, 438-459, 0096-3003 , 2018.

D. J. Anco, “Continuing consideration of co-infection and multiple pests,” APS

Features, 2018. doi:10.1094/APSFeature-2018-4.

L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, John Wiley, New York, 1962

Muhumuza, C. A mathematical model for the transmission dynamics and optimal

control strategy of Coffee Wilt disease. Diss. 2018.



How to Cite

Nyaberi, H., MUTUKU, W. ., MALONZA, D. ., GACHIGUA, G. ., & ALWORAH, G. . (2024). An optimal control model for Coffee Berry Disease and Coffee Leaf Rust co-infection. Journal of Mathematical Analysis and Modeling, 5(1), 1–25.