Spatial pattern switching enables cyclic evolution in spatial epidemics

Mathematical Model of the Role of Asymptomatic Infection in Outbreaks of Some Emerging Pathogens

Preparation for outbreaks of emerging infectious diseases is often predicated on beliefs that we will be able to understand the epidemiological nature of an outbreak early into its inception. However, since many rare emerging diseases exhibit different epidemiological behaviors from outbreak to outbreak, early and accurate estimation of the epidemiological situation may not be straightforward in all cases. Previous studies have proposed considering the role of active asymptomatic infections co-emerging and co-circulating as part of the process of emergence of a novel pathogen. Thus far, consideration of the role of asymptomatic infections in emerging disease dynamics have usually avoided considering some important sets of influences. In this paper, we present and analyze a mathematical model to explore the hypothetical scenario that some (re)emerging diseases may actually be able to maintain stable, endemic circulation successfully in an entirely asymptomatic state. We argue that an understanding of this potential mechanism for diversity in observed epidemiological dynamics may be of considerable importance in understanding and preparing for outbreaks of novel and/or emerging diseases.

Limited role of spatial self-structuring in emergent trade-offs during pathogen evolution

Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a spatially-explicit, SIR model of the latter kind proposed by Ballegooijen and Boerlijst with the aim of characterising the mechanisms causing the emergence of the trade-off and its structural robustness. Using invadability criteria, we establish the conditions under which an evolutionary feedback between transmission and virulence mediated by pattern formation can poise the system to a critical boundary separating a disordered state (without emergent trade-off) from a self-structured phase (where the trade-off emerges), and analytically calculate the functional shape of the boundary in a certain approximation. Beyond evolutionary parameters, the success of an invasion depends on the size and spatial structure of the invading and invaded populations. Spatial self-structuring is often destroyed when hosts are mobile, changing the evolutionary dynamics to those of a well-mixed population. In a metapopulation scenario, the systematic extinction of the pathogen in the disordered phase may counteract the disruptive effect of host mobility, favour pattern formation and therefore recover the emergent trade-off.

Spatial disease dynamics of free-living pathogens under pathogen predation

The epidemiological dynamics of potentially free-living pathogens are often studied with respect to a specific pathogen species (e.g., cholera) and most studies concentrate only on host-pathogen interactions. Here we show that metacommunity-level interactions can alter conventional spatial disease dynamics. We introduce a pathogen eating consumer species and investigate a deterministic epidemiological model of two habitat patches, where both patches can be occupied by hosts, pathogens, and consumers of free-living pathogens. An isolated habitat patch shows periodic disease outbreaks in the host population, arising from cyclic consumer-pathogen dynamics. On the other hand, consumer dispersal between the patches generate asymmetric disease prevalence, such that the host population in one patch stays disease-free, while disease outbreaks occur in the other patch. Such asymmetry can also arise with host dispersal, where infected hosts carry pathogens to the other patch. This indirect movement of pathogens causes also a counter-intuitive effect: decreasing morbidity in a focal patch under increasing pathogen immigration. Our results underline that community-level interactions influence disease dynamics and consistent spatial asymmetry can arise also in spatially homogeneous systems.

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Infectious diseases are a threat to human health and a hindrance to societal development. Consequently, the spread of diseases in both time and space has been widely studied, revealing the different types of spatial patterns. Transitions between patterns are an emergent property in spatial epidemics that can serve as a potential trend indicator of disease spread. Despite the usefulness of such an indicator, attempts to systematize the topic of pattern transitions have been few and far between. We present a mini-review on pattern transitions in spatial epidemics, describing the types of transitions and their underlying mechanisms. We show that pattern transitions relate to the complexity of spatial epidemics by, for example, being accompanied with phenomena such as coherence resonance and cyclic evolution. The results presented herein provide valuable insights into disease prevention and control, and may even be applicable outside epidemiology, including other branches of medical science, ecology, quantitative finance, and elsewhere.

Parasites Sustain and Enhance RNA-Like Replicators through Spatial Self-Organisation

In a prebiotic RNA world, parasitic behaviour may be favoured because template dependent replication happens in trans, thus being altruistic. Spatially extended systems are known to reduce harmful effects of parasites. Here we present a spatial system to show that evolution of replication is (indirectly) enhanced by strong parasites, and we characterise the phase transition that leads to this mode of evolution. Building on the insights of this analysis, we identify two scenarios, namely periodic disruptions and longer replication time-span, in which speciation occurs and an evolved parasite-like lineage enables the evolutionary increase of replication rates in replicators. Finally, we show that parasites co-evolving with replicators are selected to become weaker, i.e. worse templates for replication when the duration of replication is increased. We conclude that parasites may not be considered a problem for evolution in a prebiotic system, but a degree of freedom that can be exploited by evolution to enhance the evolvability of replicators, by means of emergent levels of selection.

The RNA world is a stage of evolution that preceded cellular life. In this world, RNA molecules would both replicate other RNAs and behave as templates for replication. A known evolutionary problem of this world is that selection should favour parasitic templates that do not replicate others, because they would be replicated the most. A possible solution to this problem comes from spatial self-organisation: local accumulation of parasites lead to their own local extinction, which leaves empty space for replicators to invade. We show that the spatial organisation generated by interacting replicators and parasites sets the (spatial) conditions that enhance replicase activity when parasites are stronger. Moreover, we find that the co-evolution of replicators and parasites is severely constrained by the type of spatial patterns they form, and we explore this feedback between evolution and self-organisation. We conclude that spatial self-organisation may have played a prominent role in prebiotic evolution.

History, Epidemic Evolution, and Model Burn-In for a Network of Annual Invasion: Soybean Rust

Ecological history may be an important driver of epidemics and disease emergence. We evaluated the role of history and two related concepts, the evolution of epidemics and the burn-in period required for fitting a model to epidemic observations, for the U.S. soybean rust epidemic (caused by Phakopsora pachyrhizi). This disease allows evaluation of replicate epidemics because the pathogen reinvades the United States each year. We used a new maximum likelihood estimation approach for fitting the network model based on observed U.S. epidemics. We evaluated the model burn-in period by comparing model fit based on each combination of other years of observation. When the miss error rates were weighted by 0.9 and false alarm error rates by 0.1, the mean error rate did decline, for most years, as more years were used to construct models. Models based on observations in years closer in time to the season being estimated gave lower miss error rates for later epidemic years. The weighted mean error rate was lower in backcasting than in forecasting, reflecting how the epidemic had evolved. Ongoing epidemic evolution, and potential model failure, can occur because of changes in climate, host resistance and spatial patterns, or pathogen evolution.

Interfaces with internal structures in generalized rock-paper-scissors models

In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships in the context of cyclic predator-prey models with an even number of species N≥8. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces. We identify an interesting behavior associated with the symmetric or asymmetric evolution of the interface profiles depending on whether N/2 is odd or even, respectively. We also show that the macroscopic evolution of the interface network is not very sensitive to the internal structure of the interfaces. Although this work focuses on cyclic predator-prey models with an even number of species, we argue that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models.

Host mobility drives pathogen competition in spatially structured populations

Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health regarding pathogen emergence, maintenance, and evolution. The full description of host-multipathogen systems is, however, challenged by the multiplicity of factors affecting the interaction dynamics and the resulting competition that may occur at different scales, from the within-host scale to the spatial structure and mobility of the host population. Here we study the dynamics of two competing pathogens in a structured host population and assess the impact of the mobility pattern of hosts on the pathogen competition. We model the spatial structure of the host population in terms of a metapopulation network and focus on two strains imported locally in the system and having the same transmission potential but different infectious periods. We find different scenarios leading to competitive success of either one of the strain or to the codominance of both strains in the system. The dominance of the strain characterized by the shorter or longer infectious period depends exclusively on the structure of the population and on the the mobility of hosts across patches. The proposed modeling framework allows the integration of other relevant epidemiological, environmental and demographic factors, opening the path to further mathematical and computational studies of the dynamics of multipathogen systems.