RESUMEN
Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.
Asunto(s)
Ecología , Neoplasias , Humanos , Dinámica Poblacional , Crecimiento Demográfico , Modelos BiológicosRESUMEN
Disease transmission between wild ungulates and domestic livestock is an important and challenging animal health issue. The potential for disease transmission between wildlife and livestock is notoriously difficult to estimate. The first step for estimating the potential for between-species disease transmission is to quantify proximity between individuals of different species in space and time. This study estimates second-order statistics of spatio-temporal location data from radio-collared free-ranging deer, elk and cattle in northeast Oregon. Our results indicate, that when observed simultaneously, elk and cattle occur in closer proximity to each other than what would be expected based on general space use of these species. The same is true for deer and elk but not for deer and cattle. Our analysis also demonstrates that average distances between cattle and elk are largely driven by rare events of close co-mingling between the species, which extend over several hours. Behavioral causes for these co-mingling events are currently unknown. Understanding the causes for such events will be important for designing grazing practices that minimize wildlife-livestock contacts.