How do viruses get around? A review of mathematical modeling of in-host viral transmission

Abstract

Mathematical models of within host viral infections have provided important insights into the dynamics of viral infections. There has been much progress in adding more detailed biological processes to these models, such as incorporating the immune response, drug resistance, and viral coinfections. Unfortunately, the default assumption for the majority of these models is that virus is released from infected cells, travels through extracellular space, and deposits on another cell. This mode of transmission is known as cell-free infection. However, virus can also tunnel directly from one cell to another or cause neighboring cells to fuse, processes that also pass the infection to new cells. Additionally, most models do not explicitly include the transport of virus from one cell to another when describing cell-free transmission. In this review, we examine the current state of mathematical modeling that explicitly examines transmission beyond the cell-free assumption. While mathematical models have been developed to examine these processes, there are further improvements that can be made to better capture known viral dynamics.

Keywords: Advection; Cell-free transmission; Cell-to-cell transmission; Diffusion; Syncytia formation.