Is HIV short-sighted? Insights from a multistrain nested model

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus

Human mobility networks and persistence of rapidly mutating pathogens

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in subpopulations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large scale spreading. Findings are highlighted in reference to previous works and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.Comment: 29 pages, 7 figures. Submitted for publicatio

A Simple Model of Epidemics with Pathogen Mutation

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals, (2) endemic infection (3) periodic epidemic outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.Comment: 9 pages, 11 figure

The Evolutionary Dynamics of a Rapidly Mutating Virus within and between Hosts: The Case of Hepatitis C Virus

Many pathogens associated with chronic infections evolve so rapidly that strains found late in an infection have little in common with the initial strain. This raises questions at different levels of analysis because rapid within-host evolution affects the course of an infection, but it can also affect the possibility for natural selection to act at the between-host level. We present a nested approach that incorporates within-host evolutionary dynamics of a rapidly mutating virus (hepatitis C virus) targeted by a cellular cross-reactive immune response, into an epidemiological perspective. The viral trait we follow is the replication rate of the strain initiating the infection. We find that, even for rapidly evolving viruses, the replication rate of the initial strain has a strong effect on the fitness of an infection. Moreover, infections caused by slowly replicating viruses have the highest infection fitness (i.e., lead to more secondary infections), but strains with higher replication rates tend to dominate within a host in the long-term. We also study the effect of cross-reactive immunity and viral mutation rate on infection life history traits. For instance, because of the stochastic nature of our approach, we can identify factors affecting the outcome of the infection (acute or chronic infections). Finally, we show that anti-viral treatments modify the value of the optimal initial replication rate and that the timing of the treatment administration can have public health consequences due to within-host evolution. Our results support the idea that natural selection can act on the replication rate of rapidly evolving viruses at the between-host level. It also provides a mechanistic description of within-host constraints, such as cross-reactive immunity, and shows how these constraints affect the infection fitness. This model raises questions that can be tested experimentally and underlines the necessity to consider the evolution of quantitative traits to understand the outcome and the fitness of an infection

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Epidemics with mutating infectivity on small-world networks

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation. © 2020, The Author(s)

Epidemics with mutating infectivity on small-world networks

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent's infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation

From Molecular Genetics to Phylodynamics: Evolutionary Relevance of Mutation Rates Across Viruses

Although evolution is a multifactorial process, theory posits that the speed of molecular evolution should be directly determined by the rate at which spontaneous mutations appear. To what extent these two biochemical and population-scale processes are related in nature, however, is largely unknown. Viruses are an ideal system for addressing this question because their evolution is fast enough to be observed in real time, and experimentally-determined mutation rates are abundant. This article provides statistically supported evidence that the mutation rate determines molecular evolution across all types of viruses. Properties of the viral genome such as its size and chemical composition are identified as major determinants of these rates. Furthermore, a quantitative analysis reveals that, as expected, evolution rates increase linearly with mutation rates for slowly mutating viruses. However, this relationship plateaus for fast mutating viruses. A model is proposed in which deleterious mutations impose an evolutionary speed limit and set an extinction threshold in nature. The model is consistent with data from replication kinetics, selection strength and chemical mutagenesis studies