Assessing the effect of fungicide treatment on Cocoa black pod disease in Ghana: Insight from mathematical modeling

  • Bismark Oduro California University of Pennsylvania
  • Ofosuhene O Apenteng
  • Henrietta Nkansah
Keywords: Black pod disease, fungicide treatment, sensitivity analysis, basic reproduction number


Black pod disease is caused by fungi of the species Phytophthora palmivora or Phytophthora megakarya. The disease causes darkening of affected areas of cocoa trees and/or fruits and leads to significant reduction in crop yields and decreases lifespan of the plant. This study presents a simple S_1S_2IT-type model with variable population size to assess the impact of fungicide treatment on the dynamics of the black pod disease. We do both theoretical studies and numerical simulations of the model. In particular, we analyze the existence of equilibrium points and their stability, simulate the model using data on reported black pod cases from Ghana. In addition, we perform sensitivity analysis of the basic reproduction number with respect to the model parameters. The results show that the top three parameters that govern the dynamics of the black pod disease are the treatment rate, transmission rate, and planting rate of new trees


Y. Acebo-Guerrero, A. Hernández-Rodr´ıguez, M. Heydrich-Pérez,M. El Jaziri, A. N. Hernández-Lauzardo, Management of black pod rot in cacao (Theobroma cacao L.): a review, Fruits, 67(1) pp.41–48, 2012.

S. Kolavalli, M. Vigneri, Cocoa in Ghana: Shaping the success of an economy. Yes, Africa can: success stories from a dynamic continent, pp. 201-218, 2011.

Y. Acebo-Guerrero, A. Hernández-Rodr´ıguez, O. Vandeputte, Y. Miguélez-Sierra, M. Heydrich-Pérez, L. Ye, M. El Jaziri, Characterization of Pseudomonas chlororaphis from Theobroma cacao L. rhizosphere with antagonistic activity against Phytophthora palmivora (Butler), Journal of applied microbiology, 119(4), pp.1112–1126, 2015.

A. Y. Akrofia, A. A. Appiah, I. Y. Opokua, Management of Phytophthora pod rot disease on cocoa farms in Ghana, Crop Protection, 22, pp.469–477, 2003.

M. Ndoumbe-Nkeng, C. Cilas, E. Nyemb, S. Nyassé, D. Bieysse, A. Flori, I. Sache, Impact of removing diseased pods on cocoa black pod caused by Phytophthora megakarya and on cocoa production in Cameroon, Crop Protection, 23, pp.415–424, 2004.

D. Guest, Black Pod: Diverse Pathogens with a Global Impact on Cocoa Yield, The American Phytopathological Society, 2007, doi:10.1094/PHYTO-97-12-1650.

H. C. Evans. Invertebrate vectors of Phytophthora palmivora, causing black pod disease of cocoa in Ghana, Annals of Applied Biology, 75(3), pp.331-345, 1973.

A. Y. Akrof, A. A. Appiah, I. Y. Opoku, Management of Phytophthora pod rot disease on cocoa farms in Ghana, Crop protection, 22(3), pp.469-477, 2003.

A. Ntiamoah, G. Afrane, Environmental impacts of cocoa production and processing in Ghana: life cycle assessment approach, Journal of Cleaner Production, 16(16), pp.1735-1740, 2008.

A. Laven, The risks of inclusion: Shifts in governance processes and upgrading opportunities for cocoa farmers in Ghana, https : // Amsterdam: KIT, 2010.

C. M. Brasier, M. J. Griffin, Taxonomy of Phytophthora palmivoraon cocoa, Transactions of the British Mycological Society, 72(1), pp.111-143, 1979.

R. E. Hanada, A. W. V. Pomella, H. S. Costa, J. L. Bezerra, L. L. Loguercio, J. O. Pereira, Endophytic fungal diversity in Theobroma cacao (cacao) and T. grandiflorum (cupuau) trees and their potential for growth promotion and biocontrol of black-pod disease, Fungal Biology, 114(11-12), pp. 901-910, 2010.

S. Nyassé, C. Cilas, C. Herail, G. Blaha, Leaf inoculation as an early screening test for cocoa (Theobroma cacao L.) resistance to Phytophthora black pod disease, Crop protection, 14(8), pp.657-663, 1995.

J. Palti, Cultural practices and infectious crop diseases, (Vol. 9) Springer Science and Business Media, 2012.

J. H.Bowers, B. A. Bailey, P. K. Hebbar, S. Sanogo, R. D. Lumsden, The impact of plant diseases on world chocolate production, Plant Health Progress, 10, 2001.

G. Danso-Abbeam, E. D. Setsoafia, I. G. K. Ansah, Modelling farmers investment in agrochemicals: the experience of smallholder cocoa farmers in Ghana, Research in Applied Economics, 6(4), pp. 1-16, 2014.

R. T. Awuah, In vivo use of extracts from Ocimum gratissimum and Cymbopogon citratus against Phytophthora palmivora causing blackpod disease of cocoa, Annals of applied biology, 124(1), pp.173-178, 1994.

J. D. Majer, The maintenance of the ant mosaic in Ghana cocoa farms, Journal of Applied Ecology, pp.123-144, 1976.

J. Jacobi, M. Schneider, P. Bottazzi, M. Pillco, P. Calizaya, S. Rist, Agroecosystem resilience and farmers perceptions of climate change impacts on cocoa farms in Alto Beni, Bolivia, Renewable Agriculture and Food Systems, 30(2), pp.170-183, 2015.

D. G. Gibbs, D. Leston, Insect phenology in a forest cocoa-farm locality in West Africa, Journal of Applied Ecology, pp. 519-548, 1970.

B. D. Fitt, A. D. Todd, H. A. McCartney, O. C. Macdonald, Spore dispersal and plant disease gradients; a comparison between two empirical models, Journal of Phytopathology, 118(3), pp.227-242, 1987.

L. Norgrove, S. T. E. F. A. N. Hauser, Carbon stocks in shaded Theobroma cacao farms and adjacent secondary forests of similar age in Cameroon, Tropical Ecology, 54(1), pp.15-22, 2013.

M. J. Jeger, J. Holt, F. Van Den Bosch, L. V. Madden, Epidemiology of insect?transmitted plant viruses: modelling disease dynamics and control interventions, Physiological Entomology, 29(3), pp. 291-304, 2004.

O. O. Apenteng, N. A. Ismail, A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection, PloS one, 10(7), e0131950, 2015.

N. J. Gordon, D. J. Salmond, A. F. Smith, Novel approach to nonlinear/non-Gaussian Bayesian state estimation, In IEE Proceedings F (Radar and Signal Processing) (Vol. 140, No. 2, pp. 107-113), IET Digital Library, 1993.

H. Haario, M. Laine, A. Mira, E. Saksman, DRAM: Efficient adaptive MCMC, Statistics and Computing 16: pp.339-354, 2006.

W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. Roy. Soc. Lond. A 115, pp.700-721, 1927.

W. O. Kermack and A. G. McKendrick, Contributions to the Mathematical Theory of Epidemics. II. The Problem of Endemicity, Proc. Roy. Soc. Lond. A 138: pp.55-83, 1932.

O. O. Apenteng, N. A. Ismail, Modelling the impact of migration on HIV persistency in Ghana, Stat., Optim. Inf. Comput., Vol. 7, March 2019, pp 55-65.

J. N. C. Goncalves, H. S. Rodrigues, M. T. T. Monteiro, On the dynamics of a viral marketing model with optimal control using indirect and direct methods, Stat., Optim. Inf. Comput., Vol. 6, December 2018, pp 633-644.

B. Oduro, M. J. Grijalva, W. Just, Models of Disease Vector Control: When Can Aggressive Initial Intervention Lower Long-Term Cost?, Bull. Math. Biol., Vol. 80(4), pp.788–824, 2018,

Cocoa Research Institute of Ghana,

C. Nakul, J.M. Hyman, J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol. 70, pp.1272–1296, 2008.

K. O. Okosun, O. Rachidb, N. Marcusc, Optimal control strategies and cost-effectiveness analysis of a malaria model, BioSystems. 111 pp.83–101, 2013.

B. Oduro, M. J. Grijalva, W. Just, A model of insect control with imperfect treatment, J. Biol. Dyn., 13:1, 518-537, 2019.


S. Rosa, D. F. M. Torres, Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in Florida, Stat., Optim. Inf. Comput., Vol. 6, March 2018, pp 139-149.

A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol. 69 pp.1871–1886, 2007.

L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2001.

J. P. LaSalle, Stability theory for ordinary differential equations, Journal of Differential Equations, 4, pp. 57-65, 1968.

How to Cite
Oduro, B., Apenteng, O. O., & Nkansah, H. (2020). Assessing the effect of fungicide treatment on Cocoa black pod disease in Ghana: Insight from mathematical modeling. Statistics, Optimization & Information Computing, 8(2), 374-385.
Research Articles