We propose a hybrid partial differential equation -- agent-b ased (PDE--ABM) model to describe the spatio-temporal viral dynamics in a c ell population. The virus concentration is considered as a continuous varia ble and virus movement is modelled by diffusion, while changes in the state s of cells (i.e. healthy, infected, dead) are represented by a stochastic a gent-based model. The two subsystems are intertwined: the probability of an agent getting infected in the ABM depends on the local viral concentration , and the source term of viral production in the PDE is determined by the c ells that are infected.

We develop a computational tool that allow s us to study the hybrid system and the generated spatial patterns in detai l. We systematically compare the outputs with a classical ODE system of vir al dynamics, and find that the ODE model is a good approximation only if th e diffusion coefficient is large.

We demonstrate that the model is able to predict SARS--CoV--2 infection dynamics, and replicate the output of in vitro experiments. Applying the model to influenza as well, we can ga in insight into why the outcomes of these two infections are different. DTSTAMP:20211207T194548Z DTSTART;TZID=Europe/Budapest:20210923T110000 DTEND;TZID=Europe/Budapest:20210923T123000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR