Banana Xanthomonas wilt dynamics with mixed cultivars in a periodic environment

Abstract

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.