The following sum appears in Mathematical Epidemiology in the context of the schistosomiasis:
$$\sum _{p=0}^{\infty } \left( \sum _{q=0}^{\infty }{\frac {\min \{ p,q \} {\lambda}^{p+2+q}}{ \left( p+2 \right) !\,p!\, \left( q+2 \right) !\,q!}} \right)$$
Please let me know what is and how to obtain the closed form. Many thanks.