Cordyline disease
 

Could anyone advise me on a Cordyline problem. I live in the tropics and
have Cordyline plants (mainly in full sun). They are affected by what I
think is Fusarium leaf spot. Pin prick red/brown spots develop on the leaves
as they grow. The spotting mainly occurs from half way up the leaf to the
tips. It is associated with large regions of lack of colour from the tip
down. The leaves look unsightly and die. Does anyone recognise this problem?
Can it be treated, without destroying the plants? Can I propagate from the
stems and avoid the disease?