Abstract
In this paper, we give an overview of our recent results concerning the mathematical modelling of autoimmune diseases in absence [1] and in presence [2] of immunotherapeutic treatment. Then we complement the model description given in [2], by developing here a kinetic system describing the cellular dynamics corresponding to the macroscopic model presented in [2]. This is the main new contribution in these proceedings and it allows us to investigate the effect of an external drug therapy at the cellular level. The relevant properties on existence, uniqueness, positivity and asymptotic behaviour of the solution to the new kinetic system are stated. Some numerical simulations are also performed for the models in absence and in presence of immunotherapy, to analyse both the effect of optimal treatment strategies and the sensitivity of the solutions to certain parameters of the model with biological significance.
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Acknowledgements
This work is partially supported by the Portuguese FCT Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM.
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Costa, M.F.P., Ramos, M.P.M., Ribeiro, C., Soares, A.J. (2021). Recent Developments on the Modelling of Cell Interactions in Autoimmune Diseases. In: Bernardin, C., Golse, F., Gonçalves, P., Ricci, V., Soares, A.J. (eds) From Particle Systems to Partial Differential Equations. ICPS ICPS ICPS 2019 2018 2017. Springer Proceedings in Mathematics & Statistics, vol 352. Springer, Cham. https://doi.org/10.1007/978-3-030-69784-6_8
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