Cross-scale dynamics and the evolutionary emergence of infectious diseases

Sebastian J. Schreiber; Ruian Ke; Claude Loverdo; Miran Park; Priyanna Ahsan; James O. Lloyd-Smith

Emerging infectious diseases are rising in frequency and impact and are placing a growing burden on public health and world economies [1] [2] [3] [4] . Nearly all of these emergence events involve pathogens that are exposed to novel environments such as zoonotic pathogens entering human populations from non-human animal reservoirs, or human pathogens exposed to antimicrobial drugs [1] . In these novel environments, pathogens may experience new selective forces acting at multiple biological scales, leading to reduced replication rates within hosts or less efficient transmission between hosts. When these novel environments are sufficiently harsh, emergence only occurs when the pathogen adapts sufficiently quickly to avoid extinction. As genetic sequencing of pathogens becomes increasingly widespread, there are clear signs of such rapid adaptation [5] [6] [7] [8] [9] [10] [11] , but we lack a cohesive framework to understand how this process might work across scales. Theoretical studies have shed important insights into circumstances under which this evolutionary emergence is possible, but either have focused on the host-to-host transmission dynamics and treated within-host dynamics only implicitly [12] [13] [14] [15] , or have accounted for explicit within-host dynamics only along a fixed transmission chain [16, 17] . Here, we introduce and analyze a model explicitly linking these two biological scales and demonstrate how within-host viral competition, infection duration, transmission dynamics within a host population, and the size of transmission bottlenecks determine the likelihood of evolutionary emergence. This analysis sheds new light on factors governing pathogen emergence, addresses long-standing questions about evolutionary aspects of emergence, and lays the foundation for making risk assessments which integrate outcomes from in vitro and in vivo experiments with findings from sequence-based surveillance in the field. wild-type maladapted for the novel environment and a mutant strain potentially adapted for the novel environment. The cross-scale model with explicit within-host dynamics. Formally, the cross-scale model is a continuous time, age-dependent, multi-type branching process [79, 80] . The "type" of individual corresponds to the composition of the initial virus population (i.e. the founding viral population that initiates the infection), and the "age" of an individual corresponds to the time since their initial infection. Within an infected host, the viral dynamics determine how the viral load and viral composition change over time due to competition between strains and mutation events. Transmission events are determined by the viral load and composition of the host and, consequently, are age-dependent. Below, we describe the model at each scale and the biological processes we consider in detail. The mean-field analogue of our model is an age-structured partial differential equation model introduced by Coombs et al. [73] .