Inverse problems for a class of measure dependent dynamical systems

We consider a class of probability measure dependent dynamical systems which arise in the study of multiscale phenomena in diverse fields such as immunological population dynamics, viscoelasticity of polymers and rubber, and polarization in dielectric materials. We develop an inverse problem framework for studying systems with distributed temporal delays. In particular, we establish conditions for existence and uniqueness of the forward problem and well-posedness (including method stability under numerical approximations) for the inverse problem of estimating the probability measures. We show that a motivating class of models of HIV infection dynamics satisfies all the conditions of our framework, thereby providing a theoretical foundation for inverse problem computations with these models.

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