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Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Foundation for Evolution, Medicine, and Public Health.)

We describe a multiple strain Susceptible Infected Recovered deterministic model for the spread of an influenza subtype within a population. The model incorporates appearance of new strains due to antigenic drift, and partial immunity to reinfection with related circulating strains. It also includes optional seasonal forcing of the transmission rate of the virus, which allows for comparison between temperate zones and the tropics. Our model is capable of reproducing observed qualitative patterns such as the overall annual outbreaks in the temperate region, a reduced magnitude and an increased frequency of outbreaks in the tropics, and the herald wave phenomenon. Our approach to modelling antigenic drift is novel and further modifications of this model may help improve the understanding of complex influenza dynamics. [ABSTRACT FROM AUTHOR]

Abstract: High evolvability of influenza virus and the complex nature of its antagonistic interaction with the host immune system make it difficult to predict which strain of virus will become epidemic next and when it will emerge. To investigate the most likely time at which a new successful strain emerges every year in seasonal influenza, we use an individual-based model that takes into account the seasonality in transmission rate and host cross-immunity against a current viral strain due to previous infections with other strains. Our model deals with antigenic evolution of influenza virus that originated by point mutations at amino acid sites that constitute epitope and is driven by host immune response. Under the range of parameters by which influenza virus shows a “trunk” shape in its phylogenetic tree, as is typical in influenza A virus evolution, we find that most successful mutant strains emerge in an early part of the epidemic season, and that the time when the number of infected hosts reaches a maximum tends to be more than one season after viral emergence. This carryover of the epidemic peak timing implies that we can predict the strain that will become dominant in the epidemic in the following year. [Copyright &y& Elsevier]

Abstract: A new deterministic model for the transmission dynamics of two strains of influenza is designed and used to qualitatively assess the role of cross-immunity on the transmission process. It is shown that incomplete cross-immunity could induce the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The model undergoes competitive exclusion (where Strain drives out Strain to extinction whenever ). For the case where infection with one strain confers complete immunity against infection with the other strain, it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the reproduction number is less than unity. In the absence of cross-immunity, the model can have a continuum of co-existence endemic equilibria (which is shown to be globally-asymptotically stable for a special case). When infection with one strain confers incomplete immunity against the other, numerical simulations of the model show that the two strains co-exist, with Strain dominating (but not driving out Strain ), whenever . [Copyright &y& Elsevier]

As blood-sucking parasites, ticks inflict great damage to animals and humans in many parts of the world. The continued use of chemical acaricides is not sustainable due to increasing tick resistance, growing public concern over drug residues in food and in the environment, and the high cost of developing new acaricides. Therefore, an alternative control strategy is urgently needed. Vaccines against ticks have been shown to be functionally feasible, as highlighted by the success of Bm86 vaccines against Rhipicephalus (Boophilus) microplus and closely related tick species. However, a limited number of tick antigens with cross-protective epitopes have been characterized so far, limiting widespread deployment of the available vaccines, including those derived from Bm86. Therefore, identifying tick antigens with potential broad-spectrum protection against multiple tick species is subject of vigorous research at present. In this paper, progress towards effective anti-tick vaccines is reviewed in the light of emerging data from studies including heterologous tick challenge. Taken together, these studies indicate that the decades-long search for a universal tick vaccine is making progress, with such a vaccine likely to be based on multiple cross-reactive antigens. [ABSTRACT FROM AUTHOR]

Abstract: When multiple infections are possible during an individual’s lifetime, as with influenza, a host’s history of infection and immunity will determine the result of future exposures. In turn, the suite of varying individual infection histories will shape the population level dynamics of the disease. Exploring the consequences of precisely how immunity is acquired using mathematical models has proven challenging though: if strains have circulated previously, there are combinations of past infection to consider. However, by using an age-structured mathematical model of a disease with multiple strains, we can examine the population immune profile without explicitly keeping track of all possible infection histories. This framework allows previously unknown consequences of assumptions about immune acquisition to be observed. In particular, we see that ‘original antigenic sin’ can reduce immunity in some age groups: these immune blind spots could be responsible for the unexpectedly high severity of certain past influenza epidemics. [Copyright &y& Elsevier]

This study presents a continuous-time model for the sylvatic transmission dynamics of two strains of Trypanosoma cruzi enzootic in North America, in order to study the role that adaptations of each strain to distinct modes of transmission (classical stercorarian transmission on the one hand, and vertical and oral transmission on the other) may play in the competition between the two strains. A deterministic model incorporating contact process saturation predicts competitive exclusion, and reproductive numbers for the infection provide a framework for evaluating the competition in terms of adaptive trade-off between distinct transmission modes. Results highlight the importance of oral transmission in mediating the competition between horizontal (stercorarian) and vertical transmission; its presence as a competing contact process advantages vertical transmission even without adaptation to oral transmission, but such adaptation appears necessary to explain the persistence of (vertically-adapted) T. cruzi IV in raccoons and woodrats in the southeastern United States. [ABSTRACT FROM PUBLISHER]

Abstract: We considered a Susceptible-Infective-Recovered-Susceptible (SIRS) model with strain mutation and cross-immunity in a non-spatial model and a lattice-structured model, where all individuals can reproduce if the space/resources allow. In the lattice-structured model, both the host reproduction and pathogen transmission processes are assumed to interact with next nearest neighbors, and the model was analyzed by an improved pair approximation (IPA). A family of correlated equations of pair approximation and mean-field were presented. We show the phase diagram of the coexistence and extinction which were obtained from parameterization by measuring the basic reproduction numbers of the strains during their infection processes. The qualitative results of the pair approximation model are similar to that of the corresponding non-spatial model. Furthermore, the spatial model predicts coexistence over a wider range of parameters than the non-spatial model. In particular, when the strain evolution tends to a larger basic reproduction number, the correlated spatial approximation could predict better than the mean-field approximation. [Copyright &y& Elsevier]

It is well-known that highly pathogenic avian influenza (HPAI) strains can arise from low pathogenic strains (LPAI) during epidemics in poultry farms. Despite this, the possibility that partial cross-immunity triggered by previous exposure to LPAI viruses may reduce the pathogenicity of HPAI and thus enhance its persistence has been generally overlooked in both empirical and theoretical work on avian influenza. We propose a simple mathematical model to investigate the interacting dynamics of HPAI and LPAI strains of avian influenza in small-scale poultry farms. Through the analysis of a deterministic ordinary differential equations model, we show that: (1) for a wide range of realistic model parameters, the reduction in pathogenicity yielded by previous LPAI infection might allow an HPAI strain that would not be able to persist in a host population when alone (ℜ < 1) to invade and co-exist in the host population along with the LPAI strain and (2) the coexistence between the HPAI and LPAI strains may be characterized by multiyear periodicity. Because simulations showed that troughs between epidemics can be deep, with only a fraction of existing flocks infected by the HPAI strain, we also ran an individual-based stochastic version of the dynamical model to analyze the potential for natural fade-out of the HPAI strain. The analysis of the stochastic model confirms the prediction that previous exposure to a LPAI strain can significantly increase the duration of the epidemics by an HPAI strain before it fades from the population. [ABSTRACT FROM AUTHOR]

Abstract: Urban yellow fever and dengue coexist in Africa but not in Asia and South America. In this paper, we examine four hypotheses (and various combinations thereof) to explain the absence of yellow fever in urban areas of Asia and South America. In addition, we examine an additional hypothesis that offers an explanation of the coexistence of the infections in Africa while at the same time explaining their lack of coexistence in Asia. The hypotheses we tested to explain the nonexistence of yellow fever in Asia are the following: (1) the Asian Aedes aegypti is relatively incompetent to transmit yellow fever; (2) there would exist a competition between dengue and yellow fever viruses within the mosquitoes, as suggested by in vitro studies in which the dengue virus always wins; (3) when an A. aegypti mosquito that is infected by or latent for yellow fever acquires dengue, it becomes latent for dengue due to internal competition within the mosquito between the two viruses; (4) there is an important cross-immunity between yellow fever and other flaviviruses, dengue in particular, such that a person recovered from a bout of dengue exhibits a diminished susceptibility to yellow fever. This latter hypothesis is referred to below as the “Asian hypothesis.” Finally, we hypothesize that: (5) the coexistence of the infections in Africa is due to the low prevalence of the mosquito Aedes albopictus in Africa, as it competes with A. aegypti. We will refer to this latter hypothesis as the “African hypothesis.” We construct a model of transmission that allows all of the above hypotheses to be tested. We conclude that the Asian and the African hypotheses can explain the observed phenomena, whereas other hypotheses fail to do so. [Copyright &y& Elsevier]

Abstract: The pandemic H1N1/09 influenza virus differs from seasonal influenza in its greater prevalence among younger individuals. It is well known that younger individuals interact with one another and society as a whole more than older individuals, suggesting that this could account for the skewed prevalence. However, the observed skewed disease prevalence could also be due to a lesser biological vulnerability (cross-immunity or partial immunity) in the older generation. We develop an age-structured, compartmental mathematical model to quantify the degree to which the skewed disease prevalence among younger individuals is due to a lesser biological vulnerability in the older generation. The model incorporates synthetic data regarding sociological interaction between different age groups generated from the simulation software EpiSims, which allows a clear distinction of the sociological and biological susceptibility effects on the transmission rate of the disease. After fitting the model to available data, we quantify the degree of biological susceptibility of five age groups in the population of the United States. Our model indicates that individuals over the age of 60 are 1/15 as susceptible to H1N1/09 influenza as those under 30 years of age. The key feature in the model is separating social contact factors of disease transmission from biological ones. [Copyright &y& Elsevier]

Abstract: The paper reviews the infectivity, cross-immunization experiments, and cattle vaccination of Zimbabwean cattle-derived Theileria parva (Boleni) sporozoite stabilates produced at the Central Veterinary Laboratory (CVL) in Harare between 1980 and 2003. The Boleni stock was first isolated in July 1978 during a theileriosis outbreak and was shown to be virulent in susceptible cattle. Thereafter, the reactions observed in susceptible cattle produced by different tick stabilates derived from the original have been mostly severe (76%) or moderate (24%). The parasite concentrations in the Boleni vaccine, the vaccines used in East Africa, and a Malawian stock were compared. The infective Theileria sporozoite concentration in 1ml of stabilate in the Muguga and Serengeti (from East Africa) and Kasoba (from Malawi) vaccines were 8×, 9×, and 14× the concentration of the Boleni stabilate, respectively. The Boleni strain, like the other Zimbabwean T. parva isolates, produces a characteristic low piroplasm parasitaemia of usually less than 1% in susceptible cattle. This has largely contributed to the difference in infection rates (1963; average 40%) among tick batches used to prepare the various stabilates. Subsequently, the sporozoite concentrations in 1ml of stabilate also varied considerably (6–91; average 53), making the reproducibility and standardization of the stabilates for immunization difficult. Immunization of cattle using Boleni stabilates with oxytetracycline therapy or with titrated low doses without treatment was found to be safe and efficacious. Cross-immunity experiments demonstrated that T. parva Boleni stabilates cross-protected against all the Zimbabwean cattle-derived T. parva stocks tested. The characteristics of the Boleni stock in affording a wide spectrum of cross-protection make it an excellent candidate for cattle immunization in Zimbabwe, hence protecting the country from the introduction of foreign vaccines and subsequently, foreign parasite populations. [Copyright &y& Elsevier]

Abstract: Consumer-resource dynamics of hosts with their pathogens are modulated by complex interactions between various branches of hosts’ immune systems and the imperfectly perceived pathogen. Multistrain SIR models tend to sweep competitive interaction terms between different pathogen strains into a single parameter representing cross-immunity. After reviewing several hypotheses about the generation of immune responses, we look into the consequences of assuming that hosts with identical immune repertoires respond to new pathogens identically. In particular, we vary the breadth of the typical immune response, or the average number of pathogen epitopes a host perceives, and the probability of perceiving a particular epitope. The latter quantity in our model is equivalent both to the degree of diversity in host responses at the population level and the relative immunodominance of different epitopes. We find that a sharp transition to strain coexistence occurs as host responses become narrow or skewed toward one epitope. Increasing the breadth of the immune response and the immunogenicity of different epitopes typically increases the range of cross-immunity values in which chaotic strain dynamics and competitive exclusion occur. Models attempting to predict the outcomes of strain competition should thus consider the potential diversity and specificity of hosts’ responses to infection. [ABSTRACT FROM AUTHOR]

Abstract: Modern advances in genetic analysis have made it feasible to ascertain the variant type of a pathogen infecting a host. Classification of pathogen variants is commonly performed by clustering analysis of the observed genetic divergence among the variants. A natural question arises whether the genetically distinct variants are epidemiologically distinct. A broader question is whether the different variants constitute separate microbial species or represent minor variations of the same species. These important issues were addressed in the context of analyzing dynamics of genetically distinct variants of Bartonella bacteria in cotton rat hosts. Frequencies of acquiring a new variant were measured in relation to the genetic differences between variants successively infecting an individual rodent host. Two statistical techniques were introduced for performing such analysis, and the methodologies were illustrated with a set of data collected from a particular multi-strain Bartonella system. We carried out a frequency analysis of co-infection patterns, and a Markov chain analysis of panels of successive mixed infection time series for testing some particular gene-based grouping of the Bartonella variants with a panel of observed disease data from a rodent population. Our analysis suggests that the three genogroups A, B and C of Bartonella function as independent species but the variants within each genogroup enjoy some cross-immunity against each other. The newly developed methodologies are broadly applicable for analyzing other multi-strain pathogen data which are increasingly collected for diverse infectious diseases. [ABSTRACT FROM AUTHOR]

Abstract: Viruses that do not cause life-long immunity persist by evolving rapidly in response to prevailing host immunity. The immune-escape mutants emerge frequently, displacing or co-circulating with native strains even though mutations conferring immune evasion are often detrimental to viral replication. The epidemiological dynamics of immune-escape in acute-infection viruses with high transmissibility have been interpreted mainly through immunity dynamics at the host population level, despite the fact that immune-escape evolution involves dynamical processes that feedback across the within- and between-host scales. To address this gap, we use a nested model of within- and between-host infection dynamics to examine how the interaction of viral replication rate and cross-immunity imprint host population immunity, which in turn determines viral immune escape. Our explicit consideration of direct and immune-mediated competitive interactions between strains within-hosts revealed three insights pertaining to risk and control of viral immune-escape: (1) replication rate and immune-stimulation deficiencies (i.e., original antigenic sin) act synergistically to increase immune escape, (2) immune-escape mutants with replication deficiencies relative to their wildtype progenitor are most successful under moderate cross-immunity and frequent re-infections, and (3) the immunity profile along short host-transmission chains (local host-network structure) is a key determinant of immune escape. [Copyright &y& Elsevier]

Abstract: A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model. [Copyright &y& Elsevier]

Abstract: The 1918–1919 influenza pandemic was composed of multiple waves within a period of nine months in several regions of the world. Increasing our understanding of the mechanisms responsible for this multi-wave profile has important public health implications. We model the transmission dynamics of two strains of influenza interacting via cross-immunity to simulate two temporal waves of influenza and explore the impact of the basic reproduction number, as a measure of transmissibility associated to each influenza strain, cross-immunity and the timing of the onset of the second influenza epidemic on the pandemic profile. We use time series of case notifications during the 1918 influenza pandemic in Geneva, Switzerland, for illustration. We calibrate our mathematical model to the initial wave of infection to estimate the basic reproduction number of the first wave and the corresponding timing of onset of the second influenza variant. We use this information to explore the impact of cross-immunity levels on the dynamics of the second wave of influenza. Our results for the 1918 pandemic in Geneva, Switzerland, indicate that a second wave can occur whenever or when cross-immunity levels are less than 0.58 for our estimated of 2.4. We also explore qualitatively profiles of two-wave pandemics and compare them with real temporal profiles of the 1918 influenza pandemic in other regions of the world including several Scandinavian cities, New York City, England and Wales, and Sydney, Australia. Pandemic profiles are classified into three broad categories namely “right-handed”, “left-handed”, and “M-shape”. Our results indicate that avoiding a second influenza epidemic is plausible given sufficient levels of cross-protection are attained via natural infection during an early (herald) wave of infection or vaccination campaigns prior to a second wave. Furthermore, interventions aimed at mitigating the first pandemic wave may be counterproductive by increasing the chances of a second wave of infection that could potentially be more virulent than the first. [Copyright &y& Elsevier]

We introduce a general framework to study the dynamics of multiple strain pathogens that can impart cross–immunity through a variety of structures. We propose two types of immunity and apply them to assess the dynamics of two competing strains. We illustrate this framework using two "visions": the next–to–kin protection (NTKP) approach which assumes that strains confer cross–immunity to next in order (neighboring) strains, while providing no protection against all other strains; and the differential protection (DP) approach assumes that individuals randomly gain partial (may be reinfected) and full cross-immunity following an infection with respective probabilities. We show that the risk of infection with a particular strain is significantly higher in the DP model that the NKTP. Moreover, we demonstrate that weaker cross-immunity structures in these models are more likely to lead to instability (sustained oscillations) in the strain coexistence mode. That is, periodic oscillations are sustained in the two-strain DP model for intermediate to weak levels of cross-immunity, while the NTKP model requires at least three strains to support these unstable dynamics. [ABSTRACT FROM AUTHOR]

Abstract. Epidemiological models concerned with the control of malaria using interventions such as bed nets and vaccines increasingly incorporate realistic aspects of malaria biology. The increasing complexity of these models limits their ability to abstract ecological processes and to address questions on the regulation of population dynamics using time-series data, particularly in regards to interactions between different pathogens and the regulatory role of innate (bottom-up) and acquired (top-down) immunity. We use a theoretical framework to test hypotheses on the importance of population-level immunity and parasite abundance in regulating the population dynamics of malaria. We use qualitative loop analyses to examine the sign of the interaction between Plasmodium falciparuin and P. vivax at the population level, and we discuss implications of this sign for the within-host regulation of parasites. Our analyses of monthly malaria time-series data from the island of Espirito Santo, Vanuatu (1983-1997), show that the dynamics of P. falciparum are not sensitive to P. vivax, whereas infections by the latter increase in response to those of the former. These results support a differential use of resources inside the hosts, a resource-consumer interaction between hosts and their immune system, and within-host regulation of parasites. Finally; our results emphasize the need to better understand factors regulating malaria dynamics before developing control strategies and call for the use of control strategies directed at the interruption of transmission, such as vector control and the use of bed nets. [ABSTRACT FROM AUTHOR]

Abstract: This study explores the evolutionary dynamics of pathogen virulence in a single-infection model with density-dependent mortality. Although virulence is not an adaptation of the pathogen per se, it is generally believed to be an inevitable by-product of a pathogen''s need to propagate and transmit to new hosts: an increase in virulence will parallel an increase in transmission efficacy. The exact characteristics of the trade-off curve defined by this relationship are important with respect to possible evolutionary scenarios. We conduct a critical function analysis, a method that exposes the evolutionary outcome resulting from trade-offs of arbitrary shape, and find that this simple model can display a wide variety of evolutionary dynamics; comprising multiple stable attractors, evolutionary repellors, and most notably, evolutionary branching points. We identify the conditions under which the different evolutionary outcomes are realised. Our analysis furthermore considers the evolution of coexisting strains, and identifies the trade-off characteristics that will support an evolutionarily stable dimorphic state. We find that an evolutionarily stable dimorphism may exist also in the absence of a branching point in the monomorphic state. The analysis reveals that an evolutionarily stable dimorphism will always be attracting and that no further branching is possible under this model. We discuss our results in relation to the dimension of the environmental feedback inherent in the model, and to results from previous studies and models of evolution of virulence. [Copyright &y& Elsevier]

Abstract: Natural infection with Mycobacterium tuberculosis, as well as cross-immune reactions with the constituent of standard vaccines, attenuated M. bovis, and other species of mycobacteria confer partial immunity to subsequent M. tuberculosis infection. It has been shown in the past that the immune response to mycobacteria found naturally in the environment reduces the benefit of vaccination as assessed by means of vaccine efficacy. In this paper we show that efficacy is a poor measure of the potential success of new anti-tuberculous vaccines due to its inability to account for the relative weight of reinfection in disease dynamics. We advocate instead the use of vaccine effectiveness when evaluating the impact of new control methods against infections that confer partial immunity. Through the study of a simple model that incorporates cross-reactive responses to environmental mycobacteria (EM) and reinfection, we show how the particulars of the relation between EM abundance and vaccine effectiveness depend on the degree of protection conferred respectively by natural infection, vaccination and EM. The relative importance of reinfection as a transmission mechanism comes up as the most important source of variability in vaccine effectiveness. Our results suggest that control efforts should be placed in reducing the importance of reinfection through diminishing transmission rates. Vaccines that overcome preexisting immunity to other mycobacteria will still have varying degrees of success depending on the underlying rate of TB transmission. [Copyright &y& Elsevier]

Abstract: Resonance in seasonally forced SIR epidemiological models may lead to stable solutions in which the epidemic period is an integer multiple of the forcing period. We examine the influence of immune cross-protection and cross-enhancement on the epidemic phase relationship of resonance solutions in an annually forced two-strain SIR model. Solutions with epidemics of the two strains in-phase commonly occur for wide ranges of cross-reaction intensity. Solutions with epidemics out-of-phase are less common and limited to narrow ranges of cross-reaction intensity. This is broadly as predicted by the two natural periods of the system. The natural period corresponding to out-of-phase solutions is sensitive to changes in the cross-reaction parameter but the natural period corresponding to in-phase solutions is constant. Bifurcation analysis indicates that the stability of in-phase orbits is controlled by pitchfork and period doubling bifurcations while out-of-phase orbits may also be influenced by Andronov–Hopf bifurcations. In order to develop an intuitive understanding of the epidemiological factors governing the occurrence of different solutions we consider how the susceptible, infected and removed components of the system must interact to form a stable solution. This shows that the impact of cross-reaction is moderated by in-phase structures but amplified by out-of-phase structures. Although the average infection rate over long time periods is not affected by phase structure, this analysis indicates that in-phase epidemic patterns are likely to be more consistent and thus allow more effective health care management. [Copyright &y& Elsevier]

Abstract: A pathogen''s route to survival involves various mechanisms including its ability to invade (host''s susceptibility) and its reproductive success within an invaded host (“infectiousness”). The immunological history of an individual often plays an important role in reducing host susceptibility or it helps the host mount a faster immunological response de facto reducing infectiousness. The cross-immunity generated by prior infections to influenza A strains from the same subtype provide a significant example. The results of this paper are based on the analytical study of a two-strain epidemic model that incorporates host isolation (during primary infection) and cross-immunity to study the role of invasion mediated cross-immunity in a population where a precursor related strain (within the same subtype, i.e. H3N2, H1N1) has already become established. An uncertainty and sensitivity analysis is carried out on the ability of the invading strain to survive for given cross-immunity levels. Our findings indicate that it is possible to support coexistence even in the case when invading strains are “unfit”, that is, when the basic reproduction number of the invading strain is less than one. However, such scenarios are possible only in the presence of isolation. That is, appropriate increments in isolation rates and weak cross-immunity can facilitate the survival of less fit strains. The development of “flu” vaccines that minimally enhance herd cross-immunity levels may, by increasing genotype diversity, help facilitate the generation and survival of novel strains. [Copyright &y& Elsevier]

Abstract: Eight of nine cats inoculated with strain ME-49 and challenged with three different strains of Toxoplasma were immune to oocyst shedding, as ascertained with bioassays of their feces. In a second experiment, only toxoplasma asexual stages were seen in H&E stained gut sections of cats treated with suppressive doses of sulfamerazine and pyrimethamine starting 2 days after oral inoculation with cysts of the strain ME-49 and killed 6 days later. In a third experiment, four cats were similarly inoculated and treated for 20 days. Six weeks later, the cats received an oral homologous challenge with cysts, and none shed toxoplasma oocysts. An acceptable level of cross-protection was achieved with strain ME-49, and therefore, it can be used as a candidate strain from which antigens could be tested for enteric protection. [Copyright &y& Elsevier]

Dengue virus, the causative agent of dengue fever and its more serious manifestation dengue hemorrhagic fever, is widespread throughout tropical and subtropical regions. The virus exists as four distinct serotypes, all of which have cocirculated in Bangkok for several decades with epidemic outbreaks occurring every 8–10 years. We analyze time-series data of monthly infection incidence, revealing a distinctive pattern with epidemics of serotypes 1, 2, and 3 occurring at approximately the same time and an isolated epidemic of serotype 4 occurring in the intervening years. Phylogenetic analysis of virus samples collected over the same period shows that clade replacement events are linked to the epidemic cycle and indicates that there is an interserotypic immune reaction. Using an epidemic model with stochastic seasonal forcing showing 8- to 10-year epidemic oscillations, we demonstrate that moderate cross-protective immunity gives rise to persistent out-of-phase oscillations similar to those observed in the data, but that strong or weak cross-protection or cross-enhancement only produces in-phase patterns. This behavior suggests that the epidemic pattern observed in Bangkok is the result of cross-protective immunity and may be significantly altered by changes in the interserotypic immune reaction. [ABSTRACT FROM AUTHOR]

Abstract: Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is sufficiently complex, admits several cluster structures of different types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organisation having many features in common with pattern formation. [Copyright &y& Elsevier]

Viruses like the human immunodeficiency virus (HIV), the hepatitis B virus (HBV), the hepatitis C virus (HCV) and many others undergo numerous rounds of inaccurate reproduction within an infected host. The resulting viral quasispecies is heterogeneous and sensitive to any selection pressure. Here we extend earlier work by showing that for a wide class of models describing the interaction between the virus population and the immune system, virus evolution has a well-defined direction toward increased pathogenicity. In particular, we study virus-induced impairment of the immune response and certain cross-reactive stimulation of specific immune responses. For eight different mathematical models, we show that virus evolution reduces the equilibrium abundance of uninfected cells and increases the rate at which uninfected cells are infected. Thus, in general, virus evolution makes things worse. An idea for combating HIV infection, however, is constructing a virus mutant that could outcompete the existing infection without being pathogenic itself. [Copyright &y& Elsevier]

We studied immune responses of the jird Meriones crassus to different flea species belonging to the same family. We used jirds maintained in an outdoor enclosure (enclosure; N=18) and parasitized by fleas Xenopsylla conformis mycerini and Xenopsylla ramesis, and also jirds born in the laboratory to previously parasitized mothers (laboratory animals; N=23). We asked (i) whether cross-immunity to different fleas occurs, (ii) whether there is a sex difference in immune responses to flea parasitism and (iii) whether the severity of the immune responses depends on parasite load. In the enclosure animals, immune response to antigen from the unfamiliar flea Synosternus cleopatrae pyramidis did not differ from those to antigens from the familiar fleas. In contrast, laboratory rodents demonstrated no difference in the immune response between S. c. pyramidis antigen and either the phytohemagglutinin treatment or controls, although their responses to antigens of fleas familiar to their mothers (X. c. mycerini and X. ramesis) were significantly higher than those to antigen of S. c. pyramidis and phytohemagglutinin. The results clearly demonstrated that (i) cross-reactivity in rodent responses to different flea species occurred for enclosure but not for laboratory jirds and (ii) immune-naïve animals whose mothers were parasitized by fleas had some degree of immunity against fleas. The only sex difference in immunological parameters was the higher level of circulating immune complexes in females than in males. Only phagocytic activity was affected by flea burden, decreasing with an increase in flea numbers. [ABSTRACT FROM AUTHOR]

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic. [Copyright &y& Elsevier]

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease. [Copyright &y& Elsevier]

We study dynamical behavior and bifurcation structure of a multi-strain SIR epidemiological model with seasonal forcing in transmission rate. The conventional single strain SIR dynamics with seasonal forcing is known to show a cascade of bifurcations as the strength of seasonality increases. In this study with an extension to multiple strains of pathogens, we first investigate the bifurcation patterns of the two strain SIR model. In the two strain SIR model, a new parameter called cross-immunity between strains plays a key role in the dynamical behavior. As analogous to the single strain model, we found that the period doubling bifurcation occurs as the strength of seasonal forcing is increased. However, bifurcation patterns differ greatly both in their subharmonic periods and the relative phase of cycles between strains, depending mostly on the degree of the cross-immunity between strains. With strong and weak cross-immunities, the period doubling cascade proceeds gradually toward chaotic cycles. On the other hand, with intermediate cross-immunity, the loss of stability of annual cycle attractor is immediately followed by chaotic cycles. Asynchronous cycles of two strains are robust outcome when annual cycles lose stability, but the population can converge to perfectly synchronized biennial cycles if two strains are antigenically distant from each other. Second, we found that there are simultaneously stable multiple attractors in two strain SIR model. Biennial and chaotic attractors, e.g., occasionally coexist at the same degree of seasonal forcing, and the trajectories converge to one of them depending on the initial conditions. Such multiple attractors are widely seen between biennial and annual cycles, or among the different types of biennial cycles, at the same strength of the seasonality. Finally, we found that the population may switch from one attractor to another by introducing a small random noise in seasonally varying transmission rate. [Copyright &y& Elsevier]

We develop a model that describes the dynamics of a finite number of strains that confer partial cross-protection among strains. The immunity structure of the host population is captured by an index-set notation where the index specifies the set of strains to which the host has been exposed. This notation allows us to derive threshold conditions for the invasion of a new strain and to show the existence of an endemic multi-strain equilibrium in a special case. The dynamics of systems consisting of more than two strains can exhibit sustained oscillations caused by an overshoot in the immunity to a specific strain if cross-protection is sufficiently strong. [ABSTRACT FROM AUTHOR]

Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations. [ABSTRACT FROM AUTHOR]

• We developed a multi-strain dengue virus model with cross-immunity. • We proved the stability of disease-free equilibrium and two boundary equilibria. • We proved the existence and uniqueness of interior equilibrium. • We found that the model undergoes backward bifurcation. • We optimized the mitigation strategies, taking into account corresponding costs. Since infection with one of the five strains of dengue virus produces life-long immunity to only this strain and temporary cross-immunity to other strains, we incorporated cross-immunity and exposed states for humans and mosquitoes in our compartmental model. We proved the globally and locally asymptotic stability of the disease-free equilibrium, the locally asymptotic stability of two boundary equilibria with the existence of only one strain, and the existence and uniqueness of the interior equilibrium with the coexistence of two strains. In addition, we found that the backward bifurcation exists. We evaluated the impact of parameters on the basic reproduction number by sensitivity analysis, and optimized the mitigation strategies according to Pontryagin's Maximum Principle, taking into account corresponding costs. The numerical simulation results showed that increasing the economic costs may not always increase the effectiveness of optimal control, since the time for putting full control effort is shortened. [ABSTRACT FROM AUTHOR]

Previous exposure to influenza viruses confers cross-immunity against future infections with related strains. However, this is not always accounted for explicitly in mathematical models used for forecasting during influenza outbreaks. We show that, if an influenza outbreak is due to a strain that is similar to one that has emerged previously, then accounting for cross-immunity explicitly can improve the accuracy of real-time forecasts. To do this, we consider two infectious disease outbreak forecasting models. In the first (the "1-group model"), all individuals are assumed to be identical and cross-immunity is not accounted for. In the second (the "2-group model"), individuals who have previously been infected by a related strain are assumed to be less likely to experience severe disease, and therefore recover more quickly, than immunologically naive individuals. We fit both models to estimated case notification data (including symptomatic individuals as well as laboratory-confirmed cases) from Japan from the 2009 H1N1 influenza pandemic, and then generate synthetic data for a future outbreak by assuming that the 2-group model represents the epidemiology of influenza infections more accurately. We use the 1-group model (as well as the 2-group model for comparison) to generate forecasts that would be obtained in real-time as the future outbreak is ongoing, using parameter values estimated from the 2009 epidemic as informative priors, motivated by the fact that without using prior information from 2009, the forecasts are highly uncertain. In the scenario that we consider, the 1-group model only produces accurate outbreak forecasts once the peak of the epidemic has passed, even when the values of important epidemiological parameters such as the lengths of the mean incubation and infectious periods are known exactly. As a result, it is necessary to use the more epidemiologically realistic 2-group model to generate accurate forecasts. Accounting for cross-immunity driven by exposures in previous outbreaks explicitly is expected to improve the accuracy of epidemiological modelling forecasts during influenza outbreaks. • Real-time influenza epidemic forecasts made without informative parameter priors can be uncertain. • The dynamics of future epidemics will depend on the number of cross-immune individuals. • Neglecting cross-immunity in models will result in poor forecasts made in advance. • Real-time forecasts can be enhanced by using information from previous epidemics. • Using a model that accounts for cross-immunity can improve the accuracy of forecasts. [ABSTRACT FROM AUTHOR]

Since the reporting of the first cases of coronavirus in China and the publication of the first sequence of SARS-CoV-2 in December 2019, the virus has undergone numerous mutations. In Europe, the spring outbreak (March-April) was followed by a drop in the number of cases and deaths. The disease may have evolved into a milder form. The increase in PCR-positive cases in late summer 2020 did not lead to the expected increase in hospitalizations, ICU admissions, and deaths, based on the severity of the disease in the spring. This difference in disease severity could be due to factors independent of the virus or to the evolution of the virus. This review attempts to identify the mutations that have appeared since the beginning of the pandemic and their role in the temporal evolution of the pandemic. There are a cell and humoral type cross-reactivity in a large part of the population to common cold coronaviruses (HCoVs) and SARS-CoV-2. Evolutionarily important mutations and deletions have emerged in the SARS-CoV-2 genes encoding proteins that interact with the host immune system. In addition, one of the major mutations (in viral polymerase) is logically associated with a higher frequency of mutations throughout the genome. This frequency fluctuates over time and shows a peak at the time when the epidemic was most active. The rate of mutations in proteins involved in the relationship to the immune system continues to increase after the first outbreak. The cross-reactivity on the 1 hand and the viral mutations observed on the other hand could explain the evolution of the pandemic until the summer of 2020, partly due to the evolution of the virus in relation to the host immune system. The immunization campaign began in December 2020: concerns are emerging about a possible escape of the circulating variants vaccines in early 2021. These variants could also escape immunity acquired through infection with the 2020 strains., (© 2021 S. Karger AG, Basel.)