In this paper, we study a deterministic model with non-autonomous system for mixed cultivars to assess the effect of cultivar susceptibility and seasonal variation on banana Xanthomonas wilt (BXW) disease dynamics. A special case of two cultivars classified as highly susceptible for inflorescence infection (ABB) and less susceptible (AAA) cultivar is considered. The basic reproduction number corresponding to the non-autonomous system is derived and numerically computed to determine disease dynamics. Results showed that the disease dies out whenever the periodic basic reproduction number is less than unity and a periodic solution is obtained when it is greater than one. Results further showed that for both cultivars, the basic reproduction number increases with increasing values of the transmission rates and declines exponentially with increasing values of roguing rates. The critical roguing rate of ABB-genome cultivar was higher than that of AAA-genome cultivars. The peaks in disease prevalence indicate the importance of effective implementation of controls during the rainy season. We conclude that highly susceptible cultivars play an important role in the spread of BXW and control measures should be effectively implemented during the rainy season if BXW is to be eradicated.

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References

1. N. Bacaër and S. Guernaoui, The epidemc threshold of vector-borne diseases with seasonality: The case od cutaneous leishmaniasis in Chichaoua, Morocco, J. Math. Biol. 53 (2006) 421–436. Crossref, Web of Science, Google Scholar
2. F. Bagamba, E. Kikulwe, W. K. Tushemereirwe, D. Ngambeki, J. Muhangi, G. H. Kagezi, P. E. Ragama and S. E. Green, Awareness of banana bacterial wilt control in Uganda: 1. Farmers’ perspective, Afr. Crop Sci. J. 14 (2006) 157–164. Google Scholar
3. Banana, Banana (1996), https://www.crfg.org/pubs/ff/banana.html. Google Scholar
4. M. Biruma, M. Pillay, L. Tripathi, G. Blomme, S. Abele, M. Mwangi, R. Bandyopadhyay, P. Muchunguzi, S. Kassim, M. Nyine, L. Turyagenda and S. E. Green, Banana Xanthomonas wilt: A review of the disease management strategies and future research directions, Afr. J. Biotechnol. 6 (2007) 953–962. Google Scholar
5. G. Blomme, L. F. Turyagenda, H. Mukasa, F. Sekiwoko, S. Mpiira and S. Eden-Green, The effect of the prompt removal of inflorescence-infected plants and early debudding of inflorescences on the control of Xanthomonas wilt of banana, Acta Hortic. 828 (2009) 51–56. Crossref, Google Scholar
6. B. A. Carter, R. Reeder, S. R. Mgenzi, Z. M. Kinyua, J. N. Mbaka, K. Doyle, V. Nakato, M. Mwangi, F. Beed, V. Aritua, M. L. L. A. A. Miller and J. J. Smith, Identification of Xanthomonas vasicola (formerly X. campestris pv. musacearum), causative organism of banana Xanthomonas wilt in Tanzania and Kenya and Burundi, Plant Pathol. 59 (2010) 403. Crossref, Web of Science, Google Scholar
7. S. F. Dowell, Seasonal variation in host susceptibility and cycles of certain infectious diseases, Emerg. Infect. Dis. 7(3) (2001) 369–374. Crossref, Web of Science, Google Scholar
8. P. V. D. Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48. Crossref, Web of Science, Google Scholar
9. G. H. Kagezi, A. Kangire, W. K. Tushemereirwe, F. Bagamba, E. Kikulwe, J. Muhangi, C. Gold and P. Ragama, Banana bacterial wilt incidence in Uganda, Afr. Crop Sci. J. 14 (2006) 83–91. Google Scholar
10. W. London and J. Yorke, Recurrent outbreaks of measles, chickenpox and mumps: Seasonal variation in contact rates, Amer. J. Epidemiol. 98(6) (1978) 453–468. Crossref, Web of Science, Google Scholar
11. Y. Ma, M. Liu, Q. Hou and J. Zhao, Modelling seasonal HFMD with recessive infection in Shandong, China, Math. Biosci. Engrg. 10(4) (2013) 1159–1171. Crossref, Web of Science, Google Scholar
12. C. Mitchell and C. Kribs, A comparison of methods for calculating the basic reproduction number for periodic epidemic systems, Bull. Math. Biol. 79(8) (2017) 1846–1869. Crossref, Web of Science, Google Scholar
13. Daily Monitor, Wednesday 1 April 2016, Fighting the banana bacterial wilt. Google Scholar
14. M. Mwangi, W. Tinzaara, V. Ndungo, F. Namu, P. Ragama and B. Ranajit, Comparative study of banana Xanthomonas wilt spread in mid and high altitudes of the Great Lakes region of Africa, in Conference on International Agricultural Research for Development, University of Bonn (2006), pp. 1–12. Google Scholar
15. J. Nakakawa, J. Y. T. Mugisha, M. W. Shaw and E. Karamura, A mathematical model for the dynamics of banana Xanthomonas wilt with vertical transmission and inflorescence infection, J. Biol. Syst. 24(1) (2016) 147–165. Link, Web of Science, Google Scholar
16. V. Ndungo, S. E. Green, G. Blomme, J. Crozier and J. J. Smith, Presence of banana Xanthomonas wilt (Xanthomonas campestris pv. musacearum) in the Democratic Republic of Congo (DRC), Plant Pathol. 55 (2006) 294. Crossref, Web of Science, Google Scholar
17. W. Ocimati, F. Ssekiwoko, E. Karamura, W. Tinzaara, S. Eden-Green and G. Blomme, 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 (2013) 777–785. Crossref, Web of Science, Google Scholar
18. D. Posny and J. Wang, Modelling cholera in periodic environments, J. Biol. Dyn. 8(1) (2014) 1–19. Crossref, Web of Science, Google Scholar
19. R. H. Reeder, J. B. Muhinyuza, O. Opolot, V. Aritua, J. Crozier and J. Smith, Presence of banana bacterial wilt (Xanthomonas campestris pv. musacearum) in Rwanda, Plant Pathol. 56 (2007) 1038. Crossref, Web of Science, Google Scholar
20. F. Sekiwoko, L. F. Turyagenda, H. Mukasa, S. Eden-Green and G. Blomme, Spread of Xanthomonas campestris pv. musacearum in banana (Musa ssp.) plants following infection of the male inflorescence, Acta Hortic. 879 (2010) 349–353. Crossref, Google Scholar
21. W. Tinzaara, C. S. Gold, F. Sekiwoko, W. K. Tushemereirwe, R. Brandyopadhyay, A. Abera, and S. J. E. Green, Role of insects in the transmission of banana bacterial wilt, Afr. Crop Sci. J. 14 (2006) 105–110. Google Scholar
22. L. Tripathi, M. Mwangi, V. Aritua, W. K. Tushemereirwe, S. Abele and R. Bandyopadhyay, Xanthomonas wilt: A threat to banana Production in East and Central Africa, Plant Dis. 93 (2009) 440–451. Crossref, Web of Science, Google Scholar
23. L. Tripathi and J. N. Tripathi, Relative susceptibility of banana cultivars to Xanthomonas campestris pv. musacearum, Afr. J. Biotechnol. 8 (2009) 5343–5350. Google Scholar
24. W. K. Tushemereirwe, O. Okaasai, J. Kubiriba, C. Nankinga, J. Muhangi, N. Odoi and E. Opio, Status of banana bacterial wilt in Uganda, Afr. Crop Sci. J. 14 (2006) 73–82. Google Scholar
25. W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Eqs. 20 (2008) 699–717. Crossref, Web of Science, Google Scholar
26. C. L. Wesley and L. J. S. Allen, The basic reproduction number in epidemic models with periodic demographics, J. Biol. Dyn. 3(2–3) (2010) 116–129. Crossref, Google Scholar
27. D. Yirgou and J. E. Bradbury, A note on wilt of banana caused by the Enset wilt organism (Xanthomonas musacearum), East Afr. Agric. Forestry J. 40(1) (1974) 111–114. Crossref, Google Scholar
28. J. Zhang, Z. Jin, G.-Q. Sun, X.-D. Sun and S. Ruan, Modeling seasonal rabies epidemics in China, Bull. Math. Biol. 74 (2012) 1226–1251. Crossref, Web of Science, Google Scholar
29. F. Zhang and X.-Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl. 325 (2007) 496–516. Crossref, Web of Science, Google Scholar
30. X.-Q. Zhao, Dynamical Systems in Population Biology (Springer, New York, 2003). Crossref, Google Scholar