No abstract

Metastases are the main reason for cancer-related deaths. Initiation of metastases, where newly seeded tumor cells expand into colonies, presents a tremendous bottleneck to metastasis formation. Despite its importance, a quantitative description of metastasis initiation and its clinical implications is lacking. Here, we set theoretical grounds for the metastatic bottleneck with a simple stochastic model. The model assumes that the proliferation-to-death rate ratio for the initiating metastatic cells increases when they are surrounded by more of their kind. For a total of 159,191 patients across 13 cancer types, we found that a single cell has an extremely low median probability of successful seeding of the order of 10 −8 . With increasing colony size, a sharp transition from very unlikely to very likely successful metastasis initiation occurs. The median metastatic bottleneck, defined as the critical colony size that marks this transition, was between 10 and 21 cells. We derived the probability of metastasis occurrence and patient outcome based on primary tumor size at diagnosis and tumor type. The model predicts that the efficacy of patient treatment depends on the primary tumor size but even more so on the severity of the metastatic bottleneck, which is estimated to largely vary between patients. We find that medical interventions aiming at tightening the bottleneck, such as immunotherapy, can be much more efficient than therapies that decrease overall tumor burden, such as chemotherapy.

The spread of severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) has raised major health policy questions. Direct transmission via respiratory droplets seems to be the dominant route of its transmission. However, indirect transmission via shared contact of contaminated objects may also occur. The contribution of each transmission route to epidemic spread might change during lock-down scenarios. Here, we simulate viral spread of an abstract epidemic considering both routes of transmission by use of a stochastic, agent-based SEIR model. We show that efficient contact tracing (CT) at a high level of incidence can stabilize daily cases independently of the transmission route long before effects of herd immunity become relevant. CT efficacy depends on the fraction of cases that do not show symptoms. Combining CT with lock-down scenarios that reduce agent mobility lowers the incidence for exclusive direct transmission scenarios and can even eradicate the epidemic. However, even for small fractions of indirect transmission, such lockdowns can impede CT efficacy and increase case numbers. These counterproductive effects can be reduced by applying measures that favor distancing over reduced mobility. In summary, we show that the efficacy of lock-downs depends on the transmission route. Our results point to the particular importance of hygiene measures during mobility lock-downs.