MVC Binding List of Objects in Object

I'm trying to dynamically build a table that needs to be bound to a ViewModel on form submission.

First item is the Action the form is submitting to. Then the Parent ViewModel and then the child ViewModel. Below those are two text fields representing the data I need bound.

When I submit the form all the other fields from the page are bound to their respective property but the complex object of ProgramViewModels is not.

What am I missing?

public ActionResult Add(AddEntityViewModel viewModel){
 Code that does something
}

 public class AddEntityViewModel
    {
    public IList<int> Counties { get; set; }
    public IList<ProgramViewModel> Programs { get; set; }
    public IList<int> Regions { get; set; }
    public string EntityName { get; set; }

    public bool IsValid()
    {
        if (string.IsNullOrEmpty(EntityName))
            return false;

        if (Counties == null || Counties.Count == 0)
            return false;

        if (Programs == null || Programs.Count == 0)
            return false;

        if (Regions == null || Regions.Count == 0)
            return false;

        return true;
    }
}

public class ProgramViewModel
{
    public int Id;
    public string SystemId;
}

<input type="hidden" id="Programs[0]__Id" name="Programs[0].Id" data-programid="3" value="3">
<input type="text" id="Programs[0]__SystemId" name="Programs[0].SystemId" style="width:100%" maxlength="50">

Update:

Changed the fields to properties after adiga's answer. But that too did not fix the issue.

public class ProgramViewModel
{
    public int Id { get; set; }
    public string SystemId { get; set; }
}