The worst case scenario could be a situation where there is extensive spread of a contagious disease (that medical authorities aren't able to effectively treat) and where the continued spread of the disease is difficult to halt.
In this case, you may find yourself confined to a secure shelter (either at home or elsewhere), avoiding all outside human contact until the 'all clear' is given. Depending on the nature of the situation, this could be a question of days, weeks or - in an extreme, but unlikely, case - even months.
By taking these steps now, you can ensure that yourself and your family can survive an extended crisis - even in the event of scarce access to water, food, communications, electricity, medical help, and so on.
There are a number of things you will need to consider when preparing for a worst case scenario:
Preparing a 'safe room' at home
Preparing water supplies
Preparing food supplies
Emergency energy, lighting and communication
Emergency survival kits
Gas masks and protective clothing
Medical, hygiene and baby supplies