I want to write a trigger to update the open task count of  leads

Trigger:

 trigger UpdateLeadOpenTasksCount on Task (after delete, after insert, after undelete, after update) {

    // Declare the variables
    public set<Id> LeadIDs = new Set<Id>();
    public list<Lead> LeadsToUpdate = new List<Lead>();
    
    // Build the list of Leads to update
    if(Trigger.isInsert || Trigger.isUnDelete || Trigger.isUpdate){
        for(Task t: Trigger.new){
            if(t.WhoId != NULL && string.valueOf(t.WhoId) != NULL && string.valueOf(t.WhoId).startsWith('00Q'))
                LeadIDs.add(t.WhoId);
        }
    }
    if(Trigger.isDelete || Trigger.isUpdate){
        for(Task t: Trigger.old){
            if(t.WhoId != NULL && string.valueOf(t.WhoId) != NULL && string.valueOf(t.WhoId).startsWith('00Q'))
                LeadIDs.add(t.WhoId);
        }
    }

    // Update the Leads
    if(LeadIDs.size()>0){
        for(Lead l: [Select l.Id, l.Open_Tasks_Count__C,
            (Select Id From Tasks where IsClosed = False)
                From Lead l where Id in :LeadIDs])
            LeadsToUpdate.add(new Lead(Id=l.Id, Open_Tasks_Count__C = l.Tasks.size()));
        update LeadsToUpdate;
    }
}

But still many leads are not updating except a few. Can anyone help on this. It needs to check each and every lead already existed and newly upcoming leads and check if there is any activity and update the count. If anyone have any other existing trigger to solve this purpose please post it along with the test code. Thank you in advance.