Optimal control of a vectored plant disease model for a crop with continuous replanting

References

• F. Al Basir, P.K. Roy, S. Ray, Impact of roguing and insecticides spraying on mosaic disease in Jatropha Curcas. Control Cybern. 46 (2017), pp. 325–344.
   Google Scholar
• O.J. Alabi, P.L. Kumar and R.A. Naidu, Cassava mosaic disease: A curse to food security in sub-saharan Africa, Online. APS, Net Features, 2011.
   Google Scholar
• L.J.S. Allen and G.E. Lahodny Jr, Extinction thresholds in deterministic and stochastic epidemic models, J. Biol. Dynam. 6 (2012), pp. 590–611. doi: 10.1080/17513758.2012.665502
   PubMed Web of Science ®Google Scholar
• O. Ariyo, A.G.O. Dixon and G. Atiri, Whitefly bemisia tabaci (homoptera: Aleyrodidae) infestation on cassava genotypes grown at different ecozones in nigeria, J. Econ. Entomol. 98 (2005), pp. 611–617. doi: 10.1093/jee/98.2.611
   PubMed Web of Science ®Google Scholar
• M.-S. Chan and M.J. Jeger, An analytical model of plant virus disease dynamics with roguing and replanting, J. Appl. Ecol. 31 (1994), pp. 413–427. doi: 10.2307/2404439
   Web of Science ®Google Scholar
• Y. Chen and J. Yang, Global stability of an sei model for plant diseases, Math. Slovaca 66 (2016), pp. 305–311.
   Web of Science ®Google Scholar
• D. Fargette and K. Vié, Simulation of the effects of host resistance, reversion, and cutting selection on incidence of african cassava mosaic virus and yield losses in cassava, Phytopathology 85 (1995), pp. 370–375. doi: 10.1094/Phyto-85-370
   Web of Science ®Google Scholar
• C. Fauquet and E. Fargette, African cassava mosaic virus: etiology, epidemiology, and control, Plant Dis. 74 (1990), pp. 404–411. doi: 10.1094/PD-74-0404
   Web of Science ®Google Scholar
• W.H. Fleming, R.W. Rishel, Deterministic and Stochastic Optimal Control (Vol. 1), Springer Science & Business Media, New York, NY, 2012.
   Google Scholar
• S. Gao, L. Xia, Y. Liu and D. Xie, A plant virus disease model with periodic environment and pulse roguing, Stud. Appl. Math. 136 (2015), pp. 357–381. doi: 10.1111/sapm.12109
   Web of Science ®Google Scholar
• M.P. Hebert, L.J. Allen, Disease outbreaks in plant-vector-virus models with vector aggregation and dispersal. Discrete Cont. Dynam. Syst. Ser. B 21 (2016), pp. 2169–2191. doi: 10.3934/dcdsb.2016042
   Web of Science ®Google Scholar
• J.A.P. Heesterbeek and M.G. Roberts, The type-reproduction number T in models for infectious disease control, Math. Biosci. 206 (2007), pp. 3–10. doi: 10.1016/j.mbs.2004.10.013
   PubMed Web of Science ®Google Scholar
• F.M. Hilker, L.J. Allen, V.A. Bokil, C.J. Briggs, Z. Feng, K.A. Garrett, L.J. Gross, F.M. Hamelin, M.J. Jeger, C.A. Manore, A.G. Power, M.G. Redinbaugh, M.A. Rúa and N.J. Cunniffe, Modeling virus coinfection to inform management of maize lethal necrosis in kenya, Phytopathology 107 (2017), pp. 1095–1108.
   PubMed Web of Science ®Google Scholar
• J. Holt, M.J. Jeger, J.M. Thresh and G.W. Otim-Nape, An epidemiological model incorporating vector population dynamics applied to African cassava mosaic virus disease, J. Appl. Ecol. 34 (1997), pp. 793–806. doi: 10.2307/2404924
   Web of Science ®Google Scholar
• M.J. Jeger, J. Holt, F. Van Den Bosch and L.V. Madden, Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions, Physiol. Entomol. 29 (2004), pp. 291–304. doi: 10.1111/j.0307-6962.2004.00394.x
   Web of Science ®Google Scholar
• M. Jeger, L.V. Madden, F. van den Bosch, Plant virus epidemiology: applications and prospects for mathematical modelling and analysis to improve understanding and disease control. Plant Dis. 102 (2018), pp. 837–854. doi: 10.1094/PDIS-04-17-0612-FE
   PubMed Web of Science ®Google Scholar
• M.R. Kelly Jr, J.H. Tien, M.C. Eisenberg and S. Lenhart, The impact of spatial arrangements on epidemic disease dynamics and intervention strategies, J. Biol. Dynam. 10 (2016), pp. 222–249. doi: 10.1080/17513758.2016.1156172
   PubMed Web of Science ®Google Scholar
• V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Ordinary Differential Equations, Vol. 1, Academic Press, New York, 1969.
   Google Scholar
• J. Legg, S. Jeremiah, H. Obiero, M. Maruthi, I. Ndyetabula, G. Okao-Okuja, H. Bouwmeester, S.Bigirimana, W. Tata-Hangy, G. Gashaka, G. Mkamilo, T. Alicai and P. Lava Kumar, Comparing the regional epidemiology of the cassava mosaic and cassava brown streak virus pandemics in africa, Virus Res. 159 (2011), pp. 161–170. doi: 10.1016/j.virusres.2011.04.018
   PubMed Web of Science ®Google Scholar
• S. Lenhart and J.T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall CRC, Boca Raton, FL, 2007.
   Google Scholar
• Y. Luo, S. Gao, D. Xie and Y. Dai, A discrete plant disease model with roguing and replanting, Adv. Differ. Equ. 2015 (2015), p. 12. doi: 10.1186/s13662-014-0332-3
   Google Scholar
• A. Mallela, S. Lenhart, N.K. Vaidya, HIV-TB co-infection treatment: modeling and optimal control theory perspectives. J. Comput. Appl. Math. 307 (2016), pp. 143–161. doi: 10.1016/j.cam.2016.02.051
   Web of Science ®Google Scholar
• S.O. Mallowa, D.K. Isutsa, A.W. Kamau and J.P. Legg, Effectiveness of phytosanitation in cassava mosaic disease management in a post-epidemic area of western kenya, ARPN J. Agr. Biol. Sci. 6 (2011), pp. 8–15.
   Google Scholar
• C.F. McQuaid, C.A. Gilligan and F. van den Bosch, Considering behaviour to ensure the success of a disease control strategy, Open Sci. 4 (2017), p. 170721.
   Google Scholar
• L.S. Pontryagin, Selected Works, Volume 4: Mathematical Theory of Optimal Processes, CRC Press, Boca Raton, 1987.
   Google Scholar
• M.G. Roberts and J.A.P. Heesterbeek, A new method to estimate the effort required to control an infectious disease, Proc. R. Soc. Lond. B 270 (2003), pp. 1359–1364. doi: 10.1098/rspb.2003.2339
   PubMed Web of Science ®Google Scholar
• S.E. Seal, M.J. Jeger and F. Van den Bosch, Begomovirus evolution and disease management, Adv. Virus Res. 67 (2006), pp. 297–316. doi: 10.1016/S0065-3527(06)67008-5
   PubMed Web of Science ®Google Scholar
• S.E. Seal, F. VandenBosch and M.J. Jeger, Factors influencing begomovirus evolution and their increasing global significance: implications for sustainable control, Crit. Rev. Plant Sci. 25 (2006), pp. 23–46. doi: 10.1080/07352680500365257
   Web of Science ®Google Scholar
• R. Shi, H. Zhao and S. Tang, Global dynamic analysis of a vector-borne plant disease model, Adv. Differ. Equ. 2014 (2014), p. 59. doi: 10.1186/1687-1847-2014-59
   Google Scholar
• Z. Shuai and P. van den Driessche, Global stability of infectious disease models using lyapunov functions, SIAM J. Appl. Math. 73 (2013), pp. 1513–1532. doi: 10.1137/120876642
   Web of Science ®Google Scholar
• J. Thresh and R. Cooter, Strategies for controlling cassava mosaic virus disease in africa, Plant Pathol.54 (2005), pp. 587–614. doi: 10.1111/j.1365-3059.2005.01282.x
   Web of Science ®Google Scholar
• F. van den Bosch and A.M. de Roos, The dynamics of infectious diseases in orchards with roguing and replanting as control strategy, J. Math. Biol. 35 (1996), pp. 129–157. doi: 10.1007/s002850050047
   Web of Science ®Google Scholar
• P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48. doi: 10.1016/S0025-5564(02)00108-6
   PubMed Web of Science ®Google Scholar
• E. Venturino, P.K. Roy, F. Al Basir and A. Datta, A model for the control of the mosaic virus disease in jatropha curcas plantations, Energ. Ecol. Environ. 1 (2016), pp. 360–369. doi: 10.1007/s40974-016-0033-8
   Google Scholar
• X.S. Zhang, J. Holt and J. Colvin, A general model of plant-virus disease infection incorporating vector aggregation, Plant Pathol. 49 (2000), pp. 435–444. doi: 10.1046/j.1365-3059.2000.00469.x
   Web of Science ®Google Scholar