The evolution of virulence in sexually transmitted HIV/AIDS

A fractional-order model with different strains of COVID-19

This study examines the dynamics of COVID-19 variants using a Caputo-Fabrizio fractional order model. The reproduction ratio R 0 and equilibrium solutions are determined. The purpose of this article is to use a non-integer order derivative in order to present information about the model solutions, uniqueness, and existence using a fixed point theory. A detailed analysis of the existence and uniqueness of the model solution is conducted using fixed point theory. For the computation of the iterative solution of the model, the fractional Adams-Bashforth method is used. Using the estimated values of the model parameters, numerical results are used to support the significance of the fractional-order derivative. The graphs provide useful information about the complexity of the model, and provide reliable information about the model for any case, integer or non-integer. Also, we demonstrate that any variant with the largest basic reproduction ratio will automatically outperform the other variant.

Sexual Conflict and Sexually Transmitted Infections (STIs): Coevolution of Sexually Antagonistic Host Traits with an STI

In many taxa, there is a conflict between the sexes over mating rate. The outcome of sexually antagonistic coevolution depends on the costs of mating and natural selection against sexually antagonistic traits. A sexually transmitted infection (STI) changes the relative strength of these costs. We study the three-way evolutionary interaction among male persistence, female resistance, and STI virulence for two types of STIs: a viability-reducing STI and a reproduction-reducing STI. A viability-reducing STI escalates conflict between the sexes. This leads to increased STI virulence (i.e., full coevolution) if the costs of sexually antagonistic traits occur through viability but not through reproduction. In contrast, a reproduction-reducing STI de-escalates the sexual conflict, but STI virulence does not coevolve in response. We also investigated the establishment probability of STIs under different combinations of evolvability. Successful invasion by a viability-reducing STI becomes less likely if hosts (but not parasites) are evolvable, especially if only the female trait can evolve. A reproduction-reducing STI can almost always invade because it does not kill its host. We discuss how the evolution of host and parasite traits in a system with sexual conflict differs from a system with female mate choice.

HOST POPULATION STRUCTURE AND THE EVOLUTION OF VIRULENCE: A "LAW OF DIMINISHING RETURNS"

Structure in a population of host individuals, whether spatial or temporal, can have important effects on the transmission and evolutionary dynamics of its pathogens. One of these is to limit dispersal of pathogens and thus increase the amount of contact between a given pair or within a small group of host individuals. We introduce a "law of diminishing returns" that predicts an evolutionary decline of pathogen virulence whenever there are on average more possibilities of pathogen transmission between the same pair of hosts. Thus, the effect of repeated contact between hosts will be to shift the balance of any trade-off between virulence and transmissibility toward lower virulence.

On the principle of host evolution in host-pathogen interactions

In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion [Formula: see text]. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by their immune response stimulation rate a, we suggest that [Formula: see text] has a minimum because a trade-off exists between virulence to the host induced by the pathogen and virulence induced by the immune response. We find that the minimization of the case fatality proportion is an evolutionary stable strategy for the host.

The sociality-health-fitness nexus: synthesis, conclusions and future directions

This theme issue has highlighted the links between sociality, health and fitness in a broad range of organisms, and with approaches that include field and captive studies of animals, comparative and meta-analyses, theoretical modelling and clinical and psychological studies of humans. In this concluding chapter, we synthesize the results of these diverse studies into some of the key concepts discussed in this issue, focusing on risks of infectious disease through social contact, the effects of competition in groups on susceptibility to disease, and the integration of sociality into research on life-history trade-offs. Interestingly, the studies in this issue both support pre-existing hypotheses, and in other ways challenge those hypotheses. We focus on unexpected results, including a lack of association between ectoparasites and fitness and weak results from a meta-analysis of the links between dominance rank and immune function, and place these results in a broader context. We also review relevant topics that were not covered fully in this theme issue, including self-medication and sickness behaviours, society-level defences against infectious disease, sexual selection, evolutionary medicine, implications for conservation biology and selective pressures on parasite traits. We conclude by identifying general open questions to stimulate and guide future research on the links between sociality, health and fitness.

Disease Outbreaks: Critical Biological Factors and Control Strategies

Disease outbreaks remain a major threat to human health and welfare especially in urban areas in both developed and developing countries. A large body of theoretical work has been devoted to modeling disease emergence, and critical factors that predict outbreak occurrence and severity have been proposed. In this chapter, we focus on biological factors that underlie both theoretical models and urban planning. We describe the SARS 2002–2003 pandemic as a case study of epidemic control of a human infectious disease. We then describe theoretical analyses of disease dynamics and control strategies. An important conclusion is that epidemic control will be strongly dependent on particular aspects of pathogen biology including host breadth, virulence, incubation time, and/or mutation rate. The probability, and potential cost, of future outbreaks, may be high and lessons from both past cases and theoretical work should inform urban design and policy. Interdisciplinary collaboration in planning, swiftness of information dissemination and response, and willingness to forgo personal liberties during a crisis may be key factors in resilience to infectious disease outbreaks.

Distribution and transmission of Mycobacterium tuberculosis complex lineages among children in peri-urban Kampala, Uganda

Background

To gain insight into the transmission of tuberculosis (TB) in peri-urban Kampala-Uganda, we performed a household contact study using children as a surrogate for recent transmission of Mycobacterium tuberculosis (MTB). Using this approach, we sought to understand M. tuberculosis complex (MTBC) lineage diversity, distribution and how these relate to TB transmission to exposed children.

Method

MTBC isolates from children aged ≤ 15 years, collected from 2002 to 2010 in a household-contact study, were analyzed using a LightCycler RT-PCR SNP genotyping assay (LRPS). The resultant genotypic data was used to determine associations between MTBC lineage and the children’s clinical and epidemiological characteristics.

Results and discussion

Of the 761 children surveyed, 9 % (69/761) had culture-positive TB an estimate in the range of global childhood TB; of these 71 % (49/69) were infected with an MTBC strain of the “Uganda family”, 17 % (12/69) infected with MTBC lineage 4 strains other than MTBC Uganda family and 12 % (8/69) infected with MTBC lineage 3, thereby disproportionately causing TB in the study area. Overall the data showed no correlation between the MTBC lineages studied and transmission (OR = 0.304; P-value = 0.251; CI: 95 %; 0.039-2.326) using children a proxy for TB transmission.

Conclusions

Our findings indicate that MTBC Uganda family strains are the main cause of TB in children in peri-urban Kampala. Furthermore, MTBC lineages did not differ in their transmissibility to children.

A TWO-STRAIN EPIDEMIC MODEL WITH DIFFERENTIAL SUSCEPTIBILITY AND MUTATION

A two-strain epidemic model with differential susceptibility and mutation is formulated and analyzed in this paper. The susceptible population is divided into two subgroups according to the vaccine that provides complete protection against one of the strains (strain two) but only partial against the other (strain one). The explicit formulae for the basic reproduction number and invasion reproduction number corresponding to each strain with and without mutation are derived, respectively. It is shown that there exist exclusive equilibria and coexistence equilibria, even if the reproduction number is below one. The stability of the disease-free equilibrium, strain dominance with or without mutation are investigated. The persistence of the disease is also briefly discussed. Numerical simulations are presented to illustrate the results.

Sexually transmitted infections in polygamous mating systems

Sexually transmitted infections (STIs) are often associated with chronic diseases and can have severe impacts on host reproductive success. For airborne or socially transmitted pathogens, patterns of contact by which the infection spreads tend to be dispersed and each contact may be of very short duration. By contrast, the transmission pathways for STIs are usually characterized by repeated contacts with a small subset of the population. Here we review how heterogeneity in sexual contact patterns can influence epidemiological dynamics, and present a simple model of polygyny/polyandry to illustrate the impact of biased mating systems on disease incidence and pathogen virulence.

SIV EPIDEMIC MODELS WITH AGE OF INFECTION

accination is a very important strategy for the elimination of infectious diseases. An SIV epidemic model with age of infection and vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show that the infection-free equilibrium is locally asymptotically stable if the reproductive number R0 < 1, and the endemic equilibrium is locally asymptotically stable if R0 > 1.

Modeling the competition between viruses in a complex plant-pathogen system

In this article, we propose a mathematical model that describes the competition between two plant virus strains (MAV and PAV) for both the host plant (oat) and their aphid vectors. We found that although PAV is transmitted by two aphids and MAV by only one, this fact, by itself, does not explain the complete replacement of MAV by PAV in New York State during the period from 1961 through 1976; an interpretation that is in agreement with the theories of A. G. Power. Also, although MAV wins the competition within aphids, we assumed that, in 1961, PAV mutated into a new variant such that this new variant was able to overcome MAV within the plants during a latent period. As shown below, this is sufficient to explain the swap of strains; that is, the dominant MAV was replaced by PAV, also in agreement with Power's expectations.

Optimality models in the age of experimental evolution and genomics

Optimality models have been used to predict evolution of many properties of organisms. They typically neglect genetic details, whether by necessity or design. This omission is a common source of criticism, and although this limitation of optimality is widely acknowledged, it has mostly been defended rather than evaluated for its impact. Experimental adaptation of model organisms provides a new arena for testing optimality models and for simultaneously integrating genetics. First, an experimental context with a well-researched organism allows dissection of the evolutionary process to identify causes of model failure--whether the model is wrong about genetics or selection. Second, optimality models provide a meaningful context for the process and mechanics of evolution, and thus may be used to elicit realistic genetic bases of adaptation--an especially useful augmentation to well-researched genetic systems. A few studies of microbes have begun to pioneer this new direction. Incompatibility between the assumed and actual genetics has been demonstrated to be the cause of model failure in some cases. More interestingly, evolution at the phenotypic level has sometimes matched prediction even though the adaptive mutations defy mechanisms established by decades of classic genetic studies. Integration of experimental evolutionary tests with genetics heralds a new wave for optimality models and their extensions that does not merely emphasize the forces driving evolution.

Modeling the dynamics of viral evolution considering competition within individual hosts and at population level: the effects of treatment

We consider two viral strains competing against each other within individual hosts (at cellular level) and at population level (for infecting hosts) by studying two cases. In the first case, the strains do not mutate into each other. In this case, we found that each individual in the population can be infected by only one strain and that co-existence in the population is possible only when the strain that has the greater basic intracellular reproduction number, R (0c ), has the smaller population number R (0p ). Treatment against the one strain shifts the population equilibrium toward the other strain in a complicated way (see Appendix B). In the second case, we assume that the strain that has the greater intracellular number R (0c ) can mutate into the other strain. In this case, individual hosts can be simultaneously infected by both strains (co-existence within the host). Treatment shifts the prevalence of the two strains within the hosts, depending on the mortality induced by the treatment, which is, in turn, dependent upon the doses given to each individual. The relative proportions of the strains at the population level, under treatment, depend both on the relative proportions within the hosts (which is determined by the dosage of treatment) and on the number of individuals treated per unit time, that is, the rate of treatment. Implications for cases of real diseases are briefly discussed.

RT-SHIV subpopulation dynamics in infected macaques during anti-HIV therapy

BACKGROUND

To study the dynamics of wild-type and drug-resistant HIV-1 RT variants, we developed a methodology that follows the fates of individual genomes over time within the viral quasispecies. Single genome sequences were obtained from 3 pigtail macaques infected with a recombinant simian immunodeficiency virus containing the RT coding region from HIV-1 (RT-SHIV) and treated with short-course efavirenz monotherapy 13 weeks post-infection followed by daily combination antiretroviral therapy (ART) beginning at week 17. Bioinformatics tools were constructed to trace individual genomes from the beginning of infection to the end of the treatment.

RESULTS

A well characterized challenge RT-SHIV inoculum was used to infect three monkeys. The RT-SHIV inoculum had 9 variant subpopulations and the dominant subpopulation accounted for 80% of the total genomes. In two of the three monkeys, the inoculated wild-type virus was rapidly replaced by new wild type variants. By week 13, the original dominant subpopulation in the inoculum was replaced by new dominant subpopulations, followed by emergence of variants carrying known NNRTI resistance mutations. However, during ART, virus subpopulations containing resistance mutations did not outgrow the wide-type subpopulations until a minor subpopulation carrying linked drug resistance mutations (K103N/M184I) emerged. We observed that persistent viremia during ART is primarily made up of wild type subpopulations. We also found that subpopulations carrying the V75L mutation, not known to be associated with NNRTI resistance, emerged initially in week 13 in two macaques. Eventually, all subpopulations from these two macaques carried the V75L mutation.

CONCLUSION

This study quantitatively describes virus evolution and population dynamics patterns in an animal model. The fact that wild type subpopulations remained as dominant subpopulations during ART treatment suggests that the presence or absence of at least some known drug resistant mutations may not greatly affect virus replication capacity in vivo. Additionally, the emergence and prevalence of V75L indicates that this mutation may provide the virus a selective advantage, perhaps escaping the host immure system surveillance. Our new method to quantitatively analyze viral population dynamics enabled us to observe the relative competitiveness and adaption of different viral variants and provided a valuable tool for studying HIV subpopulation emergence, persistence, and decline during ART.

Breeding Influenza: The Political Virology of Offshore Farming

  The geographic extent, xenospecificity, and clinical course of influenza A (H5N1), the bird flu strain, suggest the virus is an excellent candidate for a pandemic infection. Much attention has been paid to the virus's virology, pathogenesis and spread. In contrast, little effort has been aimed at identifying influenza's social origins. In this article, I review H5N1's phylogeographic properties, including mechanisms for its evolving virulence. The novel contribution here is the attempt to integrate these with the political economies of agribusiness and global finance. Particular effort is made to explain why H5N1 emerged in southern China in 1997. It appears the region's reservoir of near-human-specific recombinants was subjected to a phase change in opportunity structure brought about by China's newly liberalized economy. Influenza, 200 nm long, seems able to integrate selection pressures imposed by human production across continental distances, an integration any analysis of the virus should assimilate in turn.

Transient virulence of emerging pathogens

Should emerging pathogens be unusually virulent? If so, why? Existing theories of virulence evolution based on a tradeoff between high transmission rates and long infectious periods imply that epidemic growth conditions will select for higher virulence, possibly leading to a transient peak in virulence near the beginning of an epidemic. This transient selection could lead to high virulence in emerging pathogens. Using a simple model of the epidemiological and evolutionary dynamics of emerging pathogens, along with rough estimates of parameters for pathogens such as severe acute respiratory syndrome, West Nile virus and myxomatosis, we estimated the potential magnitude and timing of such transient virulence peaks. Pathogens that are moderately evolvable, highly transmissible, and highly virulent at equilibrium could briefly double their virulence during an epidemic; thus, epidemic-phase selection could contribute significantly to the virulence of emerging pathogens. In order to further assess the potential significance of this mechanism, we bring together data from the literature for the shapes of tradeoff curves for several pathogens (myxomatosis, HIV, and a parasite of Daphnia) and the level of genetic variation for virulence for one (myxomatosis). We discuss the need for better data on tradeoff curves and genetic variance in order to evaluate the plausibility of various scenarios of virulence evolution.

Unpacking β: Within-Host Dynamics and the Evolutionary Ecology of Pathogen Transmission

Rather than being fixed, pathogen transmission varies and is thus an object of natural selection. I examine how opportunities for selection on pathogen transmission depend on (a) pathogen fitness, (b) genetic variability, and (c) forces acting at within- and between-host levels. The transmission rate, β, influences processes such as epidemic spread, postepidemic fade-outs, and low-level persistence. Complexity of infection processes within hosts leads to different transmission rates among hosts and between types of pathogens (viruses, bacteria, eukaryotic Protozoa). Generality emerges, however, by “unpacking” β into within- and between-host opportunities for selection. This is illustrated by evolutionary biology of the bacterium Yersinia pestis, which causes plague in mammals, remains highly virulent and is transmitted by multiple routes, including fleas and direct contacts with infected hosts. The strength of within-host selection is manifested through infectivity, replication, pathogenicity, and dissemination from hosts. At the between-host level, responses to selection are less predictable because of environmental variation, whereas vector-borne transmission (usually by arthropods) provides additional opportunities for selection and trade-offs between vectors and hosts. In subdivided host populations, selection favors transmission before local pathogen extinction occurs, but key components (e.g. infectious periods of hosts) are determined by within-host dynamics. Pathogen transmission is often viewed in the context of transmission-virulence trade-offs, but within-host dynamics may cause host damage unrelated to transmission, and thus transmission-virulence trade-offs are not universal.

Avian flu pandemic: Can we prevent it?

Outbreaks of highly pathogenic H5N1 avian influenza in Southeast Asia, Europe and Africa have led to devastating consequences for poultry, and have resulted in numerous infections in humans. Although these infections from the animal reservoir continue to accumulate, the virus does not seem to spread extensively among humans. However, for example, a process of genetic reassortment could occur in a human who is co-infected with avian influenza A virus and a human strain of influenza A virus. The resulting new virus might then be able to easily infect humans and spread from human to human. Therefore, many experts expect the occurrence of a pandemic due to a mutant virus which can be easily transmitted among humans. Thus, currently, a major public health concern is the next influenza pandemic; yet it remains unclear how to control such a crisis. In this paper, we investigate relations between the evolution of virulence and an effectiveness of pandemic control measures after the emergence of mutant avian influenza; one is an elimination policy of infected birds with avian influenza and the other is a quarantine policy of infected humans with mutant avian influenza. We found that each of these prevention policies can be ineffective (i.e., increase human morbidity or mortality). Further, interestingly, the same intervention might, under the same conditions, increase human morbidity and decrease human mortality, or vice versa. Our practical findings are that the quarantine policy can effectively reduce both human morbidity and mortality but the elimination policy increases either human morbidity or mortality in a worst case situation.

Prevention of avian influenza epidemic: what policy should we choose?

Human-to-human transmission of the avian influenza has been extremely rarely reported, and is considered as limited, inefficient and unsustained. However, experts warn an occurrence of "mutant avian influenza", which can easily spread among humans, because the avian influenza is already endemic, in particular in Asian poultry, and it is evolving in domestic and wild birds, pigs and humans. Outbreak of such mutant avian influenza in the human world may have devastating consequences, which are comparable with these for the 1918 "Spanish influenza". In this paper we develop a mathematical model for the spread of the mutant avian influenza, and explore the effectivity of the prevention policies, namely the elimination policy which increases the effective additional death rate of the infected birds and the quarantine policy which reduces the number of infective contacts.

Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens

Infectious pathogens compete and are subject to natural selection at multiple levels. For example, viral strains compete for access to host resources within an infected host and, at the same time, compete for access to susceptible hosts within the host population. Here we propose a novel approach to study the interplay between within- and between-host competition. This approach allows for a single host to be infected by and transmit two strains of the same pathogen. We do this by nesting a model for the host-pathogen dynamics within each infected host into an epidemiological model. The nesting of models allows the between-host infectivity and mortality rates suffered by infected hosts to be functions of the disease progression at the within-host level. We present a general method for computing the basic reproduction ratio of a pathogen in such a model. We then illustrate our method using a basic model for the within-host dynamics of viral infections, embedded within the simplest susceptible-infected (SI) epidemiological model. Within this nested framework, we show that the virion production rate at the level of the cell-virus interaction leads, via within-host competition, to the presence or absence of between-host level competitive exclusion. In particular, we find that in the absence of mutation the strain that maximizes between-host fitness can outcompete all other strains. In the presence of mutation we observe a complex invasion landscape showing the possibility of coexistence. Although we emphasize the application to human viral diseases, we expect this methodology to be applicable to be many host-parasite systems.

The spread of HIV-1 subtypes B and CRF01_AE among injecting drug users in Bangkok, Thailand

The HIV epidemic among injecting drug users (IDUs) in Bangkok was initially dominated by HIV subtype B and later by the recombinant CRF01_AE. The present study investigates the distribution of the 2 variants in time and how it is affected by changes in injecting risk behavior and treatment. A mathematic model describing the spread of HIV subtype B and CRF01_AE among IDUs was developed, and data from the AIDSVAX B/E cohort of IDUs in Bangkok were used. From the model, it was calculated that during 1999 to 2003, the annual incidence of HIV was around 0.6 and 2.7 to 3.9 infections per 100 person-years for subtype B and CRF01_AE, respectively. Of the new infections, 18% and 72% are first infections with subtype B and CRF01_AE, respectively, and 9% are superinfections. With increases in risk behavior, the fraction of superinfections rises. If treatment reduces the infectivity of CRF01_AE more than that of subtype B, the fraction of subtype B infections should increase. Subtype B should remain prevalent in a small but considerable fraction of the population for a long time. Changes in risk behavior and the introduction of treatment may alter the distribution of subtypes, but CRF01_AE should remain dominant.

Lessons from previous predictions of HIV/AIDS in the United States and Japan: epidemiologic models and policy formulation

This paper critically discusses two previous studies concerned with predictions of HIV/AIDS in the United States and Japan during the early 1990s. Although the study in the US applied a historical theory, assuming normal distribution for the epidemic curve, the underlying infection process was not taken into account. In the Japan case, the true HIV incidence was estimated using the coverage ratio of previously diagnosed/undiagnosed HIV infections among AIDS cases, the assumptions of which were not supported by a firm theoretical understanding. At least partly because of failure to account for underlying mechanisms of the disease and its transmission, both studies failed to yield appropriate predictions of the future AIDS incidence. Further, in the Japan case, the importance of consistent surveillance data was not sufficiently emphasized or openly discussed and, because of this, revision of the AIDS reporting system has made it difficult to determine the total number of AIDS cases and apply a backcalculation method. Other widely accepted approaches can also fail to provide perfect predictions. Nevertheless, wrong policy direction could arise if we ignore important assumptions, methods and input data required to answer specific questions. The present paper highlights the need for appropriate assessment of specific modeling purposes and explicit listing of essential information as well as possible solutions to aid relevant policy formulation.

Modeling Within-Host Evolution of HIV: Mutation, Competition and Strain Replacement

Virus evolution during infection of a single individual is a well-known feature of disease progression in chronic viral diseases. However, the simplest models of virus competition for host resources show the existence of a single dominant strain that grows most rapidly during the initial period of infection and competitively excludes all other virus strains. Here, we examine the dynamics of strain replacement in a simple model that includes a convex trade-off between rapid virus reproduction and long-term host cell survival. Strains are structured according to their within-cell replication rate. Over the course of infection, we find a progression in the dominant strain from fast- to moderately-replicating virus strains featuring distinct jumps in the replication rate of the dominant strain over time. We completely analyze the model and provide estimates for the replication rate of the initial dominant strain and its successors. Our model lays the groundwork for more detailed models of HIV selection and mutation. We outline future directions and application of related models to other biological situations.

Subthreshold and superthreshold coexistence of pathogen variants: the impact of host age-structure

It is well known that in the most general epidemic models with multiple pathogen variants a competitive exclusion principle is valid, such that the variant with the highest reproduction number eliminates the rest. Mechanisms such as super-infection, coinfection, and cross-immunity can lead to pathogen polymorphism where multiple strains coexist. It is also known that variability of infectivity with host age can destabilize the endemic equilibrium and cause oscillations. In this article we show that the hosts' chronological age can itself lead to coexistence of microparasites in the most basic model where competitive exclusion will occur without the age structure. Moreover, the host age-structure leads to multiple subthreshold dominance equilibria, and both weakly and strongly subthreshold coexistence. We find that the two pathogens cannot cooperate to persist subthreshold if neither one of them can persist subthreshold by itself. If, however, one of them can persist subthreshold by itself, it can cause the two pathogens to coexist in a strongly subthreshold equilibrium. The second strain that persists subthreshold through the mediation of the first always has a lower virulence. Our results show that age structure in infectivity can permit the coexistence of competing pathogens when the incidence is of proportionate mixing type (frequency-dependent transmission) and at least one of the strains is virulent.

The role of trade-off shapes in the evolution of parasites in spatial host populations: an approximate analytical approach

Given the substantial changes in mixing in many populations, there is considerable interest in the role that spatial structure can play in the evolution of disease. Here we examine the role of different trade-off shapes in the evolution of parasites in a spatially structured host population where infection can occur locally or globally. We develop an approximate adaptive dynamic analytical approach, to examine how the evolutionarily stable (ES) virulence depends not only on the fraction of global infection/transmission but also on the shape of the trade-off between transmission and virulence. Our analysis can successfully predict the ES virulence found previously by simulation of the full system. The analysis confirms that when there is a linear trade-off between transmission and virulence spatial structure may lead to an ES virulence that increases as the proportion of global transmission increases. However, we also show that the ESS disappears above a threshold level of global infection, leading to maximization. In addition just below this threshold, there is the possibility of evolutionary bi-stabilities. When we assume the realistic trade-off between transmission and virulence that results in an ESS in the classical mixed model, we find that spatial structure can increase or decrease the ES virulence. A relatively high proportion of local infection reduces virulence but intermediate levels can select for higher virulence. Our work not only emphasizes the importance of spatial structure to the evolution of parasites, but also makes it clear that situations between the local and the global need to be considered. We also emphasize the key role that the shape of trade-offs plays in evolutionary outcomes.

Seasonality and the dynamics of infectious diseases

Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the best-studied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples from human and wildlife disease systems to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers. Empirical evidence points to several biologically distinct mechanisms by which seasonality can impact host-pathogen interactions, including seasonal changes in host social behaviour and contact rates, variation in encounters with infective stages in the environment, annual pulses of host births and deaths and changes in host immune defences. Mathematical models and field observations show that the strength and mechanisms of seasonality can alter the spread and persistence of infectious diseases, and that population-level responses can range from simple annual cycles to more complex multiyear fluctuations. From an applied perspective, understanding the timing and causes of seasonality offers important insights into how parasite-host systems operate, how and when parasite control measures should be applied, and how disease risks will respond to anthropogenic climate change and altered patterns of seasonality. Finally, by focusing on well-studied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.

Competition of pathogen strains leading to infection with variable infectivity and the effect of treatment

A model for the spread of two strains of a pathogen leading to an infection with variable infectivity is considered. The course of infection is described by two stages with different infectivity levels. The model is extended to account for treatment by including a third stage with different infectivity and survival for those treated. The contribution of each stage to incidence and prevalence is investigated and the effect of infectivity and survival on the basic reproduction ratio is examined. Standard equilibrium analysis is performed for both models, revealing that the successful strain is the one with highest reproduction ratio. If therapy, however, is more effective against the strain that wins in the absence of treatment and its reproduction ratio is sufficiently reduced, it might be outcompeted by the other strain after treatment becomes widely available. In this case, early introduction of treatment can prevent a major outbreak.

The coevolutionary dynamics of obligate ant social parasite systems--between prudence and antagonism

In this synthesis we apply coevolutionary models to the interactions between socially parasitic ants and their hosts. Obligate social parasite systems are ideal models for coevolution, because the close phylogenetic relationship between these parasites and their hosts results in similar evolutionary potentials, thus making mutual adaptations in a stepwise fashion especially likely to occur. The evolutionary dynamics of host-parasite interactions are influenced by a number of parameters, for example the parasite's transmission mode and rate, the genetic structure of host and parasite populations, the antagonists' migration rates, and the degree of mutual specialisation. For the three types of obligate ant social parasites, queen-tolerant and queen-intolerant inquilines and slavemakers, several of these parameters, and thus the evolutionary trajectory, are likely to differ. Because of the fundamental differences in lifestyle between these social parasite systems, coevolution should further select for different traits in the parasites and their hosts. Queen-tolerant inquilines are true parasites that exert a low selection pressure on their host, because of their rarity and the fact that they do not conduct slave raids to replenish their labour force. Due to their high degree of specialisation and the potential for vertical transmission, coevolutionary theory would predict interactions between these workerless parasites and their hosts to become even more benign over time. Queen-intolerant inquilines that kill the host queen during colony take-over are best described as parasitoids, and their reproductive success is limited by the existing worker force of the invaded host nest. These parasites should therefore evolve strategies to best exploit this fixed resource. Slavemaking ants, by contrast, act as parasites only during colony foundation, while their frequent slave raids follow a predator prey dynamic. They often exploit a number of host species at a given site, and theory predicts that their associations are best described in terms of a highly antagonistic coevolutionary arms race.

Phenotypic plasticity of host-parasite interactions in response to the route of infection

The microsporidium Octosporea bayeri can infect its host, the planktonic crustacean Daphnia magna, vertically and horizontally. The two routes differ greatly in the way the parasite leaves the harbouring host (transmission) and in the way it enters a new, susceptible host (infection). Infections resulting from each route may thus vary in the way they affect host and parasite life-histories and, subsequently, host and parasite fitness. We conducted a life-table experiment to compare D. magna infected with O. bayeri either horizontally or vertically, using three different parasite isolates. Both the infection route and the parasite isolate had significant effects on host life-history. Hosts matured at different ages depending on the parasite isolate, and at a size that varied with infection route. The frequency of host sterility and the host's life-time reproductive success were affected by both the infection route and the parasite isolate. The infection route also affected parasite life-history. The production of parasite spores was much higher in vertically than in horizontally infected hosts. We found a trade-off between the production of spores (the parasite's horizontal fitness component) and the production of infected host offspring (the parasite's vertical fitness component). This study shows that hosts and parasites can react plastically to different routes of infection, suggesting that ecological factors that may influence the relative importance of horizontal and vertical transmission can shape the evolution of host and parasite life histories, and, consequently, the evolution of virulence.

Strain replacement in an epidemic model with super-infection and perfect vaccination

Several articles in the recent literature discuss the complexities of the impact of vaccination on competing subtypes of one micro-organism. Both with competing virus strains and competing serotypes of bacteria, it has been established that vaccination has the potential to switch the competitive advantage from one of the pathogen subtypes to the other resulting in pathogen replacement. The main mechanism behind this process of substitution is thought to be the differential effectiveness of the vaccine with respect to the two competing micro-organisms. In this article, we show that, if the disease dynamics is regulated by super-infection, strain substitution may indeed occur even with perfect vaccination. In fact we discuss a two-strain epidemic model in which the first strain can infect individuals already infected by the second and, as far as vaccination is concerned, we consider a best-case scenario in which the vaccine provides perfect protection against both strains. We find out that if the reproduction number of the first strain is smaller than the reproduction number of the second strain and the first strain dominates in the absence of vaccination then increasing vaccination levels promotes coexistence which allows the first strain to persist in the population even if its vaccine-dependent reproduction number is below one. Further increase of vaccination levels induces the domination of the second strain in the population. Thus the second strain replaces the first strain. Large enough vaccination levels lead to the eradication of the disease.

The evolution of parasitic diseases

Parasites are characterized by their fitness-reducing effect on their hosts. Studying the evolution of parasitic diseases is an attempt to understand these negative effects as an adaptation of the parasite, the host, both or neither. Dieter Ebert and E. Allen Herre here discuss how the underlying concepts are general and are applicable for all types of disease-producing organisms, broadly defined here as parasites. The evolutionary processes that lead to the maintenance of the harmful effects are believed to be characterized by genetic correlations with other fitness components of the parasite. Depending on the shape of these correlations, any level of virulence can evolve.

The evolution of virulence in pathogens with frequency-dependent transmission

Frequency-dependent transmission is an important feature of diseases that are sexually transmitted or transmitted by a vector that actively searches for hosts. Here I describe the evolution of virulence in pathogens that have frequency-dependent transmission. I consider two components of virulence--an increase in host mortality due to infection, as is classically described, and a decrease in host fecundity due to infection, because frequency dependence is common among diseases that fully or partially sterilize their hosts. Theoretical predictions pertaining to host-pathogen numerical dynamics can be quite different between pathogens with frequency-dependent transmission and those with density-dependent transmission. In contrast, this study suggests that the principles governing the evolution of virulence that have been established in the context of density-dependent pathogens may also apply (qualitatively) to frequency-dependent pathogens. I examine the evolutionary trajectories of the mortality and sterility components of virulence as well as the role of spatial population structure in the evolution of the sterility component of virulence.

The curse of the pharaoh in space: free-living infectious stages and the evolution of virulence in spatially explicit populations

The idea that parasites with long-lived infective stages may evolve higher virulence has received considerable attention. This idea is called 'the curse of the pharaoh' because of the hypothesis that the death of Lord Carnavon was caused by very long-lived propagules of a highly virulent infectious disease. Here, we examined the evolution of diseases that transmit via free-living stages in a spatial context. We show that, if virulence evolves independently of transmission, long-lived infective stages can select for higher virulence. There is always the evolution of a finite transmission rate, which becomes higher when the infective stages are shorter lived. When a trade-off occurs between transmission and virulence, we show that there is no evidence for the curse of the pharaoh. Indeed, higher transmission and therefore virulence may be selected for by shorter rather than long-lived infective stages.

The effect of treatment on pathogen virulence

The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence.

The dynamics of two viral infections in a single host population with applications to hantavirus

An SI epidemic model for a host with two viral infections circulating within the population is developed, analyzed, and numerically simulated. The model is a system of four differential equations which includes a state for susceptible individuals, two states for individuals infected with a single virus, one which is vertically transmitted and the other which is horizontally transmitted, and a fourth state for individuals infected with both viruses. A general growth function with density-dependent mortality is assumed. A special case of this model, where there is no coinfection and total cross immunity, is thoroughly analyzed. Several threshold values are defined which determine establishment of the disease and persistence at equilibrium for one or both of the infections within the host population. The model has applications to a hantavirus and an arenavirus that infect cotton rats. The hantavirus is transmitted horizontally whereas the arenavirus is transmitted vertically. It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus.

Parasite transmission modes and the evolution of virulence

A mathematical model is presented that explores the relationship between transmission patterns and the evolution of virulence for horizontally transmitted parasites when only a single parasite strain can infect each host. The model is constructed by decomposing parasite transmission into two processes, the rate of contact between hosts and the probability of transmission per contact. These transmission rate components, as well as the total parasite mortality rate, are allowed to vary over the course of an infection. A general evolutionarily stable condition is presented that partitions the effects of virulence on parasite fitness into three components: fecundity benefits, mortality costs, and morbidity costs. This extension of previous theory allows us to explore the evolutionary consequences of a variety of transmission patterns. I then focus attention on a special case in which the parasite density remains approximately constant during an infection, and I demonstrate two important ways in which transmission modes can affect virulence evolution: by imposing different morbidity costs on the parasite and by altering the scheduling of parasite reproduction during an infection. Both are illustrated with examples, including one that examines the hypothesis that vector-borne parasites should be more virulent than non-vector-borne parasites (Ewald 1994). The validity of this hypothesis depends upon the way in which these two effects interact, and it need not hold in general.

Mathematical models of cross protection in the epidemiology of plant-virus diseases

ABSTRACT Mathematical models of plant-virus disease epidemics were developed where cross protection occurs between viruses or virus strains. Such cross protection can occur both naturally and through artificial intervention. Examples of diseases with continuous and discontinuous crop-host availability were considered: citrus tristeza and barley yellow dwarf, respectively. Analyses showed that, in a single host population without artificial intervention, the two categories of host plants, infected with a protecting virus alone and infected with a challenging virus, could not coexist in the long term. For disease systems with continuous host availability, the virus (strain) with the higher basic reproductive number (R(0)) always excluded the other eventually; whereas, for discontinuous systems, R(0) is undefined and the virus (strain) with the larger natural transmission rate was the one that persisted in the model formulation. With a proportion of hosts artificially inoculated with a protecting mild virus, the disease caused by a virulent virus could be depressed or eliminated, depending on the proportion. Artificial inoculation may be constant or adjusted in response to changes in disease incidence. The importance of maintaining a constant level of managed cross protection even when the disease incidence dropped was illustrated. Investigations of both pathosystem types showed the same qualitative result: that managed cross protection need not be 100% to eliminate the virulent virus (strain). In the process of replacement of one virus (strain) by another over time, the strongest competition occurred when the incidence of both viruses or virus strains was similar. Discontinuous crop-host availability provided a greater opportunity for viruses or virus strains to replace each other than did the more stable continuous cropping system. The process by which one Barley yellow dwarf virus replaced another in New York State was illustrated.

Transmission bottlenecks and the evolution of fitness in rapidly evolving RNA viruses

We explored the evolutionary importance of two factors in the adaptation of RNA viruses to their cellular hosts, size of viral inoculum used to initiate a new infection, and mode of transmission (horizontal versus vertical). Transmission bottlenecks should occur in natural populations of viruses and their profound effects on viral adaptation have been previously documented. However, the role of transmission mode has not received the same attention. Here we used a factorial experimental design to test the combined effects of inoculum (bottleneck) size and mode of transmission in evolution of vesicular stomatitis virus (VSV) in tissue culture, and compared our results to the predictions of a recent theoretical model. Our data were in accord with basic genetic principles concerning the balance between mutation, selection and genetic drift. In particular, attenuation of vertically transmitted viruses was a consequence of the random accumulation of deleterious mutations, whereas horizontally transmitted viruses experiencing similar bottlenecks did not suffer the same fitness losses because effective bottleneck size was actually determined by the number of host individuals. In addition, high levels of viral fitness in horizontally transmitted populations were explained by competition among viral variants.

Evolution of pathogen virulence: the role of variation in host phenotype

Selection on pathogens tends to favour the evolution of growth and reproductive rates and a concomitant level of virulence (damage done to the host) that maximizes pathogen fitness. Yet, because hosts often pose varying selective environments to pathogens, one level of virulence may not be appropriate for all host types. Indeed, if a level of virulence confers high fitness to the pathogen in one host phenotype but low fitness in another host phenotype, alternative virulence strategies may be maintained in the pathogen population. Such strategies can occur either as polymorphism, where different strains of pathogen evolve specialized virulence strategies in different host phenotypes or as polyphenism, where pathogens facultatively express alternative virulence strategies depending on host phenotype. Polymorphism potentially leads to specialist pathogens capable of infecting a limited range of host phenotypes, whereas polyphenism potentially leads to generalist pathogens capable of infecting a wider range of hosts. Evaluating how variation among hosts affects virulence evolution can provide insight into pathogen diversity and is critical in determining how host pathogen interactions affect the phenotypic evolution of both hosts and pathogens.