A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

1. Yirgou D, Bradbury JF, A note on wilt of banana caused by the Enset wilt organism Xanthomonas musacearum, East Afr Agric Forestry J 40:111–114, 1974. 2. Tinzaara W, Gold CS, Sekiwoko F, Tushemereirwe W, Brandyopadhyay R, Abera A, Eden-Green S, Role of insects in the transmission of banana bacterial wilt, Afr Crop Sci J 14:105–110, 2006. 3. Addis T, Turyagenda LF, Alemu T, Karamura E, Blomme G, Garden tool transmission of Xanthomonas campestris pv. musacearum on banana (Musa ssp.) and Enset in Ethopia, Acta Hortic 879:367–372, 2010. 4. Kagezi GH, Kangire A, Tushemereirwe W, Bagamba F, Kikulwe E, Muhangi J, Gold CS, Ragama P, Banana bacterial wilt incidence in Uganda, Afr Crop Sci J 14:83–91, 2006. 5. Karamura E, Kayobyo G, Tushemereirwe W, Benin S, Blomme G, Eden-Green S, Markham R, Assessing the impacts of banana bacterial wilt disease on banana (Musa spp.) productivity and livelihoods of Ugandan farm households, Acta Hortic 879:749–755, 2010. 6. Buregyeya H, Kubiriba J, Tusiime G, Kityo R, Ssekiwoko F, Tushemerierwe WK, Role of birds and bats in long distance transmission of banana bacterial wilt in Uganda, Int J Agric Innov Res 2:636–640, 2014. 7. Smith JJ, Jones DR, Karamura E, Blomme G, Turyagenda FL, An Analysis of the Risk from Xanthomonas campestris pv musacearum to Banana Cultivation in Eastern, Central and Southern Africa, Bioversity International, 2008. 8. Ssekiwoko F, Turyagyenda LF, Mukasa H, Eden-Green S, Blomme G, Systemicity of Xanthomonas campestris pv musacearum in flower-infected banana plants. pp. 789–793. In: Soprano E, Tcacenco FA, Lichtemberg LA, Silva MC (eds.). Proceedings of Reuni˜ao Internacional ACORBAT, Joinville, Santa Catarina (BRA), 2006/10/15–20. Bananicultura: um neg´ocio sustent´avel. Anais XVII reuni˜ao internacional ACORBAT. Vol. 2: Trabalhos completos [Banane: un commerce durable. M´emoires de la XVIIe A Mathematical Model for the Dynamics of Banana Xanthomonas Wilt 165 reunion ACORBAT. Vol. 2: Travaux complets] [Banana: A sustainable business. Proceedings of the XVII ACORBAT international meeting. Vol. 2: Full papers] [Bananos: Un negocio sustentable. Memorias del XVII reunion internacional ACORBAT. Vol. 2: Trabajos completos]. ACORBAT, Joinville, Santa Catarina (BRA), 2006. 9. Tripathi L, Mwangi M, Aritua V, Tushemereirwe WK, Abele S, Bandyopadhyay R,Xant homonas wilt: A threat to banana production in east and Central Africa, Plant Dis 93:440–451, 2009. 10. Biruma M, Pillay M, Tripathi L, Blomme G, Abele S, Mwangi M, Bandyopadhyay R, Muchunguzi P, Kassim S, Nyine M, Turyagenda L, Eden-Green S, Banana Xanthomonas Wilt: A review of the disease management strategies and future research directions Afr J Biotechnol 6:953–962, 2007. 11. Ocimati W, Ssekiwoko F, Karamura E, Tinzaara W, Eden-Green S, Blomme G, Systemicity of Xanthomonas campestris pv musacearum and time to disease expression after inflorescence in East African highland and Pisang Awak bananas in Uganda, Plant Pathol 62:777–785, 2012. 12. van den Driessche P, Watmough J, Reproduction numbers and sub-threshold endemic equilbria for compartmental models of disease transmission, Math Biosci 180:29–48, 2002. 13. Hale JK, Ordinary Differential Equations, John Wiley, New York, 1969. 14. Castillo-Chavez C, Song B, Dynamical models of tuberclosis and their applications, Math Biosci 2:361–404, 2004. 15. Perko L, Differential Equations and Dynamical Systems, Springer, 2000. 16. Vargas-De-Le´on C, Stability analysis of SIS epidemic model with standard incidence, Foro-Red-Mat Revista Electr´onica de Contenido Matem´atico 28:1–11, 2011. 17. Blomme G, Turyagenda LF, Mukasa H, Ssekiwoko F, Mpiira S, Eden-Green S, The effect of the prompt removal of inflorescence-infected plants and early debudding of inflorescence on the control of Xanthomonas wilt of banana, Acta Hortic 828:51–56, 2009. 18. Banana Plant Info, Available at http://www.bananaplants.net/banananinfo.html. 19. Oluwafemi AB, Influence of number of sucker per plant on the growth, yield and yield components of plantain (Musa sp) in Ado -ekiti, Nigeria, Agric Sci Res J 3:45–49,2013. 20. Chitnis N, Hyman JM, Chusing JM, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull Math Biol 70:172–1296, 2008. 21. Kubiriba J, Tushemereirwe WK, Approaches for the control of banana Xanthomonas wilt in East and Central Africa, African J Plant Sci 8:398–404, 2014