if you like typically analytically intractable math.
The humanist motivations for studying immunology are, frankly, trivial to state. But what about the motivations of scientific curiosity?
From a complex systems perspective, biological and immunological dynamics are fascinating. For example, these systems are incomprehensible with a single object, instead requiring knowledge of the entire collective dynamics. A typical analogy is often made to physics; the same exact molecules are found in ice, water, and water vapour, but we have no hope to understand phase changes without studying an Avogadro’s number of molecules (their positions and orientations) and even more so their interactions. Too, these dynamics fall into the realm of nonlinear science. Phase changes are completely nonlinear, a tiny change of temperature in the right range (e.g. 99ºC to 101ºC) elicits an incredible response whereas the same relative change in temperature in a different range is almost imperceptible (e.g. -40ºC to -50ºC). In fact, in approaching these systems, we are often hampered by our linear thinking—that a small perturbation on a system leads to a small response, an assumption that is very often untrue in complex systems.
To study them, we must resort to complicated nonlinear ODES, PDES, graph/network theoretical approaches, stochastic approaches, and above all usually computational methods. If you like the sound of these challenges, maybe theoretical immunology/biology would be a great topic of research or study.