Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

Phongchai Jittamai; Natdanai Chanlawong; Wanyok Atisattapong; Wanwarat Anlamlert; Natthiya Buensanteai; Phongchai Jittamai; Natdanai Chanlawong; Wanyok Atisattapong; Wanwarat Anlamlert; Natthiya Buensanteai

doi:10.3934/mbe.2021258

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5069-5093. doi: 10.3934/mbe.2021258

Previous Article Next Article

Research article

Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

1.
School of Industrial Engineering, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
2.
Department of Mathematics and Statistics, Thammasat University, Pathum Thani 12121, Thailand
3.
School of Crop Production Technology, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

Academic Editor: Jia Li

Received: 06 April 2021 Accepted: 31 May 2021 Published: 07 June 2021

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.
- cassava mosaic disease (CMD),
- reproduction number,
- local stability,
- global stability,
- sensitivity analysis
Citation: Phongchai Jittamai, Natdanai Chanlawong, Wanyok Atisattapong, Wanwarat Anlamlert, Natthiya Buensanteai. Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5069-5093. doi: 10.3934/mbe.2021258

Related Papers:

Abstract

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.

References

[1]	H. L. Wang, X. Y. Cui, X. W. Wang, S. S. Liu, Z. H. Zhang, X. P. Zhou, First report of Sri Lankan cassava mosaic virus infecting cassava in Cambodia, Plant Dis., 100 (2016), 1029-1029.
[2]	J. M. Thresh, G. W. Otim-Nape, J. P. Legg, D. Fargette, African cassava mosaic virus disease: the magnitude of problem, Afr. J. Root Tuber Crops, 2 (1997), 13-17.
[3]	B. Patil, C. Fauquet, Cassava mosaic geminiviruses: actual knowledge and perspectives, Mol. Plant Pathol., 10 (2009), 685-701. doi: 10.1111/j.1364-3703.2009.00559.x
[4]	J. M. Thresh, G. W. Otim-Nape, Strategies for controlling African cassava mosaic geminivirus, Adv. Dis. Vector Res., 10 (1994), 215-236. doi: 10.1007/978-1-4612-2590-4_8
[5]	K. R. Bock, Control of African cassava mosaic geminivirus by using virus-free planting material, Trop. Sci., 34 (1994), 102-109.
[6]	J. P. Legg, J. M. Thresh, Cassava mosaic virus disease in East Africa: a dynamic disease in a changing environment, Virus Res., 71 (2000), 135-149. doi: 10.1016/S0168-1702(00)00194-5
[7]	J. Holt, J. Colvin, V. Muniyappa, Identifying control strategies for tomato leaf curl virus disease using an epidemiology model, J. Appl. Ecol., 36 (1999), 625-633. doi: 10.1046/j.1365-2664.1999.00432.x
[8]	R. A. Taylor, E. A. Mordecai, C. A. Gilligan, J. R. Rohr, L. R. Johnson, Mathematical models are a powerful method to understand and control the spread of Huanglongbing, PeerJ, 71 (2016), e2642.
[9]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Math. Phys. Eng. Sci., 115 (1927), 700-721.
[10]	P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6
[11]	T. Kuniya, Numerical approximation of the basic reproduction number for a class of age-structured epidemic models, Appl. Math. Lett., 73 (2017), 106-112. doi: 10.1016/j.aml.2017.04.031
[12]	H. M. Yang, The transovarial transmission in the dynamics of dengue infection: Epidemiological implications and thresholds, Math. Biosci., 286 (2017), 1-15. doi: 10.1016/j.mbs.2017.01.006
[13]	J. Mohammed-Awel, A. B. Gumel, Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics, Math. Biosci., 312 (2019), 33-49. doi: 10.1016/j.mbs.2019.02.008
[14]	F. van den Bosh, M. J. Jeger, The basic reproduction number of vector-borne plant virus epidemics, Virus Res., 241 (2017), 196-202. doi: 10.1016/j.virusres.2017.06.014
[15]	J. M. Thresh, Progress curves of plant virus disease, Adv. Appl. Biol., 8 (1983), 1-85.
[16]	J. H. Arias, J. Gomez-Gardenes, S. Meloni, E. Estrada, Epidemics on plants: Modeling long-range dispersal on spatially embedded networks, J. Theor. Biol., 453 (2018), 1-13. doi: 10.1016/j.jtbi.2018.05.004
[17]	L. V. Madden, B. Raccah, T. P. Pirone, Modelling plant disease increase as a function of vector numbers: Nonpersistent viruses, Res. Popul. Ecol., 32 (1990), 47-65. doi: 10.1007/BF02512589
[18]	M. J. Jeger, F. van den Bosch, L. V. Madden, Modelling virus- and host-limitation in vectored plant disease epidemics, Virus Res., 159 (2011), 215-222. doi: 10.1016/j.virusres.2011.05.012
[19]	B. Buonomo, The effect of time delay in plant-pathogen interactions with host demography, Math. Biosci. Eng., 12 (2015), 473-490. doi: 10.3934/mbe.2015.12.473
[20]	D. Fargette, M. J. Jeger, C. Fauquet, L. D. C. Fishpool, Analysis of temporal disease progress of African cassava mosaic virus, Phytopathology, 84 (1994), 91-98. doi: 10.1094/Phyto-84-91
[21]	J. Holt, M. J. Jeger, J. M. Thresh, G. W. Otim-Nape, An epidemiology model incorporating vector population dynamics applied to African cassava mosaic virus disease, J. Appl. Ecol., 34 (1997), 793-806. doi: 10.2307/2404924
[22]	T. Kinene, L. Luboobi, B. Nannyonga, G. G. Mwanga, A mathematical model for the dynamics and cost effectiveness of the current control of cassava brown streak disease in Uganda, J. Math. Comput. Sci., 5 (2015), 567-600.
[23]	K. R. Bock, R. D. Woods, Etiology of African cassava mosaic disease, Plant Dis., 67 (1983), 994-995. doi: 10.1094/PD-67-994
[24]	J. P. Legg, Emergence, spread and strategies for controlling the pandemic of cassava mosaic virus disease in east and central Africa, Crop Prot., 18 (1999), 627-637. doi: 10.1016/S0261-2194(99)00062-9
[25]	V. A. Bokil, L. J. S. Allen, M. J. Jeger, A. Lenhart, Optimal control of a vectored plant disease model for a crop with continuous replanting, J. Biol. Dyn., 13 (2019), 325-353. doi: 10.1080/17513758.2019.1622808
[26]	X. S. Zhang, J. Holt, J. Colvin, Synergism between plant viruses: a mathematical analysis of the epidemiological implications, Plant Pathol., 50 (2001), 723-746.
[27]	H. W. Hethcote, An immunization model for a heterogeneous population, Theor. Popul. Biol., 14 (1978), 338-349. doi: 10.1016/0040-5809(78)90011-4
[28]	M. J. Jeger, F. van den Bosch, L. V. Madden, J. Holt, A model for analyzing plant-virus transmission characteristics and epidemic development, IMA J. Math. Appl. Med. Biol., 15 (1998), 1-18. doi: 10.1093/imammb/15.1.1
[29]	H. Wagaba, G. Beyene, C. Trembley, T. Alicai, C. M. Fauquet, N. J. Taylor, Efficient transmission of cassava brown streak disease viral pathogens by chip bud grafting, BMC Res. Notes, 6 (2013), 516. doi: 10.1186/1756-0500-6-516
[30]	M. Jeger, J. Holt, F. van den Bosch, L. Madden, Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions, Physiol. Entomol., 29 (2004), 291-304. doi: 10.1111/j.0307-6962.2004.00394.x
[31]	T. C. Reluga, J. Medlock, A. Galvani, The discounted reproductive number for epidemiology, Math. Biosci. Eng., 6 (2009), 377-393. doi: 10.3934/mbe.2009.6.377
[32]	K. Sato, Basic reproduction number of SEIRS model on regular lattice, Math. Biosci. Eng., 16 (2019), 6708-6727. doi: 10.3934/mbe.2019335
[33]	C. V. de León, J. A. C. Hernández, Local and global stability of host-vector disease models, Revi. Elec. Cont. Mat., 25 (2008), 1-9.
[34]	F. Zhou, Y. Hongxing, Global dynamics of a host-vector-predator mathematical model, J. Appl. Math., 2014 (2014), 1-10.
[35]	X. Wang, H. Wang, M. Y. Li, $R_0$ and sensitivity analysis of a predator-prey model with seasonality and maturation delay, Math. Biosci., 315 (2019), 108225. doi: 10.1016/j.mbs.2019.108225
[36]	M. L. M. Manyombe, J. Mbang, J. Lubuma, B. Tsanou, Global dynamics of a vaccination model for infectious diseases with asymptomatic carries, Math. Biosci. Eng., 13 (2016), 813-840. doi: 10.3934/mbe.2016019
[37]	I. Ghosh, P. K. Tiwari, S. Mandal, M. Martcheva, J. Chattopadhyay, A mathematical study to control Guinea worm disease: a case study on Chad, J. Biol. Dyn., 12 (2018), 846-871. doi: 10.1080/17513758.2018.1529829
[38]	S. Ullah, M. F. Khan, S. A. A. Shah, M. Farooq, M. A. Khan, M. bin Mamat, Optimal control analysis of vector-host model with saturated treatment, Eur. Phys. J. Plus, 135 (2020), 839. doi: 10.1140/epjp/s13360-020-00855-1
[39]	K. O. Okosun, R. Ouifki, N. Marcus, Optimal control analysis of a Malaria disease transmission model that includes treatment and vaccination with waning immunity, BioSystems, 106 (2011), 136-145. doi: 10.1016/j.biosystems.2011.07.006

Reader Comments

your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)