Envision that a particular virus, chicken pox, has just entered the body. We might need millions of B and T cells to combat this virus. But, we only have a few B cells and a few T cells currently in the body that can recognize chicken pox virus.
In a brief description, what has to happen?

The whole situation will stimulate the Adaptive Immunity system along with Humoral responses.  As the individual is lacking both B and T cells, therefore the virus will be able to make infection by causing the disease.

Explanation:

Chickenpox has a particular antigen. It will act as an epitope that interacts with the particular sites of the lymphocyte. The epitope will stimulate the Adaptive Immunity system. The antigen will activate both B and T cells.  

Here 2 cases can happen.  

If the individual has experienced the disease before then Secondary Immune Response is gonna happen. B cells will be able to recognize those antigens and will secrete more antibodies in respect to that antigen particularly. T cells will also gonna bind with antigens and will secrete cytotoxic T cells which will fight against those antigens. If the individual is experiencing the disease for the first time then Primary Immune Response is gonna happen. B cells will take much more time to recognize the kind of antigens. Then it will give T cell the information about the antigen and will produce the antibody accordingly. As the individual is lacking both B and T cells, therefore the virus will be able to make infection by causing the disease.