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We propose and investigate general kinetic models %of Boltzmann type withtransition probabilities that can describe the simultaneous change of multiplemicroscopic states of the interacting agents. These models can be applied tomany problems in socio-economic sciences, where individuals may change boththeir compartment and their characteristic kinetic variable, as for instancekinetic models for epidemics or for international trade with possible transfersof agents. Mathematical properties of our kinetic model are proved, asexistence and uniqueness of a solution for the Cauchy problem in suitableWasserstein spaces. The quasi-invariant asymptotic regime, leading to simplerkinetic Fokker-Planck-type equations, is investigated and commented on incomparison with other existing models. Some numerical tests are performed inorder to show time evolution of distribution functions and of meaningfulmacroscopic fields, even in case of non-constant interaction probabilities.

Kinetic models for systems of interacting agents with multiple microscopic states