The effect of contact heterogeneity and multiple routes of transmission on final epidemic size

Heterogeneity in the number of potentially infectious contacts amongst members of a population increases the basic reproduction ratio (R(0)) and markedly alters disease dynamics compared to traditional mean-field models. Most models describing transmission on contact networks only account for one specific route of transmission. However, for many infectious diseases multiple routes of transmission exist. The model presented here captures transmission through a well defined network of contacts, complemented by mean-field type transmission amongst the nodes of the network that accounts for alternative routes of transmission. The impact of these combined transmission mechanisms on the final epidemic size is investigated analytically. The analytic predictions for the purely mean-field case and the transmission through the network-only case are confirmed by individual-based network simulations. There is a critical transmission potential above which an increased contribution of the mean-field type transmission increases the final epidemic size while an increased contribution of the transmission through the network decreases it. Below the critical transmission potential the opposite effect is observed.     

Quantifying the Routes of Transmission for Pandemic Influenza

Motivated by the desire to assess nonpharmaceutical interventions for pandemic influenza, we seek in this study to quantify the routes of transmission for this disease. We construct a mathematical model of aerosol (i.e., droplet-nuclei) and contact transmission of influenza within a household containing one infected. An analysis of this model in conjunction with influenza and rhinovirus data suggests that aerosol transmission is far more dominant than contact transmission for influenza. We also consider a separate model of a close expiratory event, and find that a close cough is unlikely (≈1% probability) to generate traditional droplet transmission (i.e., direct deposition on the mucous membranes), although a close, unprotected and horizontally-directed sneeze is potent enough to cause droplet transmission. There are insufficient data on the frequency of close expiratory events to assess the relative importance of aerosol transmission and droplet transmission, and it is prudent to leave open the possibility that droplet transmission is important until proven otherwise. However, the rarity of close, unprotected and horizontally-directed sneezes—coupled with the evidence of significant aerosol and contact transmission for rhinovirus and our comparison of hazard rates for rhinovirus and influenza—leads us to suspect that aerosol transmission is the dominant mode of transmission for influenza.     

Microsporidian life cycles and diversity: the relationship between virulence and transmission

The microsporidia are obligate intracellular parasites which have diverse life cycles involving both horizontal and vertical transmission and parasitise a wide range of vertebrate and invertebrate hosts. In this paper we consider the life cycles and diversity of the microsporidia. We focus in particular on the relationship between parasite transmission and virulence and its implications for host-parasite coevolution. The use of horizontal and vertical routes of transmission varies between species and there is a strong link between transmission and virulence. Horizontal transmission is characterised by a high parasite burden and associated pathogenicity. In contrast, vertical transmission is characterised by low virulence, which has led to under-reporting of this important transmission route. Vertically transmitted microsporidia may also cause male killing or feminisation of their host, with implications for host population sex ratio and stability. Phylogenetic analysis shows that vertical transmission occurs in diverse branches of the Microspora. We find that there is evidence for vertical transmission in both vertebrate and invertebrate hosts and conclude that it is a common or possibly even ubiquitous transmission route within this phylum.     

The effect of transmission route on plant virus epidemic development and disease control

A model for indirect vector transmission and epidemic development of plant viruses is extended to consider direct transmission through vector mating. A basic reproduction number is derived which is the sum of the R₀ values specific for three transmission routes. We analyse the model to determine the effect of direct transmission on plant disease control directed against indirect transmission. Increasing the rate of horizontal sexual transmission means that vector control rate or indirect transmission rate must be increased/decreased substantially to maintain R₀ at a value less than 1. By contrast, proportionately increasing the probability of transovarial transmission has little effect. Expressions are derived for the steady-state values of the viruliferous vector population. There is clear advantage for an insect virus in indirect transmission to plants, especially where the sexual and transovarial transmission rates are low; however information on virulence-transmissibility relationships is required to explain the evolution of a plant virus from an insect virus.     

Unidirectional Optical Transmission of a Dual Metallic Grating with Grooves

In this paper, a dual grating structure for unidirectional transmission is presented. The forward and backward transmission performances have been investigated by finite element method. To enhance the forward transmission and to suppress the backward transmission simultaneously, we suggested to cut grooves on the surfaces of one of the gratings, and the effects of the grooves on the optical transmission have been studied. The numerical simulation results reveal that the transmission contrast ratio and the optical unidirectional transmission of the structure can be improved markedly by properly arranging the size and the position of the grooves. The forward transmission can be more than 90%, while the backward transmission transmittance is less than 5%.

     

Magnetic Force Transmission of a Reciprocating Motion

Magnetic force transmission of a reciprocating motion is studied by theoretical analysis and experiment. A mathematical model for calculating the magnetic force is derived using the theory of equivalent magnetic charges. An experimental rig is constructed to test the transmission and the model is verified by experiment. Effect of the transmission parameters on the magnetic force is analyzed theoretically from the model, and characteristic of the transmission is studied experimentally. Since the transmission is without direct contact between two elements, it is suitable for application in an organism.     

Malaria transmission-blocking vaccines: the bonus of effective malaria control

Reduction of transmission is important for effective malaria control. Standard microscopic detection grossly underestimates the human transmission reservoir. Malaria transmission intensity is defined by local and focal conditions. Transmission-blocking vaccines may be effective by directly targeting identified hot spots of transmission.     

THE EVOLUTION OF VIRULENCE IN PATHOGENS WITH VERTICAL AND HORIZONTAL TRANSMISSION

The idea that vertical transmission of parasites selects for lower virulence is widely accepted. However, little theoretical work has considered the evolution of virulence for parasites with mixed horizontal plus vertical transmission. Many human, animal, and plant parasites are transmitted both vertically and horizontally, and some horizontal transmission is generally necessary to maintain parasites at all. We present a population-dynamical model for the evolution of virulence when both vertical and horizontal transmission are present. In the simplest such model, up to two infectious strains can coexist within one host population. Virulent, vertically transmitted pathogens can persist in a population when they provide protection against more virulent, horizontally transmitted strains. When virulence is maintained by a correlation with horizontal transmission rates, increased levels of vertical transmission always lower the evolutionarily stable (ESS) level of virulence. Contrary to existing theory, however, increases in opportunities for horizontal transmission also lower the ESS level of virulence. We explain these findings in light of earlier work and confirm them in simulations including imperfect vertical transmission. We describe further simulations, in which both vertical and horizontal transmission rates are allowed to evolve. The outcome of these simulations depends on whether high levels of vertical transmission are possible with low virulence. Finally, we argue against the notion of a virulence-avirulence continuum between horizontal and vertical transmission, and discuss our results in relation to empirical studies of transmission and virulence.     

Models of multifactorial inheritance: IV, asymmetric transmission for a scalar phenotype

The influence of asymmetric transmission is more finely studied in this paper. We focus on cases of (i) equal parental transmission not necessarily midparental; (ii) maternal and paternal distinguished transmission including the case of strict uniparental transmission; (iii) different levels of transmission depending on the offspring sex; and others. The explicit equilibrium covariance structure is worked out and a number of qualitative properties of the equilibrium variances are delineated as functions of the model parameters.     

Acephaline gregarine parasites (Monocystis sp.) are not transmitted sexually among their lumbricid earthworm hosts

The precise transmission mode(s) of acephaline gregarines in their earthworm hosts has long been questioned, yet a rigorous experimental evaluation of sexual transmission is currently lacking. That Monocystis sp., a common gregarine parasite of the earthworm Lumbricus terrestris, infects the sexual organs of its host is suggestive of sexual transmission. Considering the divergent evolutionary consequences of various modes of transmission, excluding or proving sexual transmission in this host-parasite system is critical to fully understanding it. We cultured uninfected earthworms from cocoons and subsequently mated them to either an infected or uninfected partner (from the wild). We then compared these individuals with an orally infected group, which were infected using a newly developed gavage (oral injection) method. Our data have unambiguously established that (1) horizontal sexual transmission does not play a significant role in the transmission of Monocystis sp., and (2) oral transmission through the soil is likely the principal mode of transmission between earthworms. This finding is important to models of mate-choice because infection avoidance does not appear to drive mating decisions. Finally, we further report a successful and relatively simple method to obtain infection-free individuals, which can subsequently be infected via oral gavage and used in empirical studies.     

Contact transmission of Tobacco mosaic virus: a quantitative analysis of parameters relevant for virus evolution

Transmission between hosts is required for the maintenance of parasites in the host population and determines their ultimate evolutionary success. The transmission ability of parasites conditions their evolution in two ways: on one side, it affects the genetic structure of founded populations in new hosts. On the other side, parasite traits that increase transmission efficiency will be selected for. Therefore, knowledge of the factors and parameters that determine transmission efficiency is critical to predict the evolution of parasites. For plant viruses, little is known about the parameters of contact transmission, a major way of transmission of important virus genera and species. Here, we analyze the factors determining the efficiency of contact transmission of Tobacco mosaic virus (TMV) that may affect virus evolution. As it has been reported for other modes of transmission, the rate of TMV transmission by contact depended on the contact opportunities between an infected and a noninfected host. However, TMV contact transmission differed from other modes of transmission, in that a positive correlation between the virus titer in the source leaf and the rate of transmission was not found within the range of our experimental conditions. Other factors associated with the nature of the source leaf, such as leaf age and the way in which it was infected, had an effect on the rate of transmission. Importantly, contact transmission resulted in severe bottlenecks, which did not depend on the host susceptibility to infection. Interestingly, the effective number of founders initiating the infection of a new host was highly similar to that reported for aphid-transmitted plant viruses, suggesting that this trait has evolved to an optimum value.     

Persistence of an infectious disease in a subdivided population

The transmission dynamics of a communicable disease in a subdivided population where the spread among groups follows the proportionate mixing model while the within-group transmission can correspond to preferred mixing, proportionate mixing among subgroups, or mixing between social and nonsocial subgroups, is analyzed. It is shown that the threshold condition for the disease to persist is that either (i) the disease can persist within at least one group through intragroup contacts, or--if (i) does not hold--(ii) the intergroup transmission is sufficiently high. The among-group transmission is computed as an average where each subgroup's reproductive number is weighted according to its intragroup activity level squared and the total number of cases that one infectious individual will cause through intragroup contacts. The model thus allows for a study of the relative importance of communitywide disease transmission and of disease transmission within geographically or socially separate groups.     

Interactions between frequency-dependent and vertical transmission in host-parasite systems.

We investigate host-pathogen dynamics and conditions for coexistence in two models incorporating frequency-dependent horizontal transmission in conjunction with vertical transmission. The first model combines frequency-dependent and uniparental vertical transmission, while the second addresses parasites transmitted vertically via both parents. For the first model, we ask how the addition of vertical transmission changes the coexistence criteria for parasites transmitted by a frequency-dependent horizontal route, and show that vertical transmission significantly broadens the conditions for parasite invasion. Host-parasite coexistence is further affected by the form of density-dependent host regulation. Numerical analyses demonstrate that within a host population, a parasite strain with horizontal frequency-dependent transmission can be driven to extinction by a parasite strain that is additionally transmitted vertically for a wide range of parameters. Although models of asexual host populations predict that vertical transmission alone cannot maintain a parasite over time, analysis of our second model shows that vertical transmission via both male and female parents can maintain a parasite at a stable equilibrium. These results correspond with the frequent co-occurrence of vertical with sexual transmission in nature and suggest that these transmission modes can lead to host-pathogen coexistence for a wide range of systems involving hosts with high reproductive rates.     

Timing of exposure is critical in a highly sensitive model of SARS-CoV-2 transmission

Transmission efficiency is a critical factor determining the size of an outbreak of infectious disease. Indeed, the propensity of SARS-CoV-2 to transmit among humans precipitated and continues to sustain the COVID-19 pandemic. Nevertheless, the number of new cases among contacts is highly variable and underlying reasons for wide-ranging transmission outcomes remain unclear. Here, we evaluated viral spread in golden Syrian hamsters to define the impact of temporal and environmental conditions on the efficiency of SARS-CoV-2 transmission through the air. Our data show that exposure periods as brief as one hour are sufficient to support robust transmission. However, the timing after infection is critical for transmission success, with the highest frequency of transmission to contacts occurring at times of peak viral load in the donor animals. Relative humidity and temperature had no detectable impact on transmission when exposures were carried out with optimal timing and high inoculation dose. However, contrary to expectation, trends observed with sub-optimal exposure timing and lower inoculation dose suggest improved transmission at high relative humidity or high temperature. In sum, among the conditions tested, our data reveal the timing of exposure to be the strongest determinant of SARS-CoV-2 transmission success and implicate viral load as an important driver of transmission.     

Malaria transmission and morbidity

Stable malaria endemicity is maintained over a wide range of transmission intensities in sub-Saharan Africa. This paper considers variations in the clinical manifestations and their consequences with differences in transmission intensity. Epidemiological approaches to malarial disease have concentrated on two clinical syndromes, severe malarial anaemia and cerebral malaria. Within an area the mean age of children with severe malarial anaemia is always lower than that of those with cerebral malaria. In areas of higher malaria transmission children, on average, encounter malaria at a younger age and the mean age of clinical cases is lower. Malarial anaemia tends therefore to be relatively more important under high transmission settings and cerebral malaria tends to gain in importance under lower transmission settings. In a number of studies the total load of malaria morbidity, whether measured as none severe malaria in the community or as severe malaria admitted to hospital, is low under stable low transmission conditions but is at its highest under moderate intensities of transmission. Thereafter it reaches a plateau, or even falls, at the highest transmission intensities. It is not known whether the same is true for mortality in communities living under different transmission settings. Possible implications for changes in patterns of morbidity and mortality following interventions which lower malaria transmission are discussed. It is concluded that such interventions should play an important role in integrated malaria control programmes but that these should involve concomitant introduction of other interventions, in order to minimise the possible risks of a reduced effect as the immune response of the population re-equilibrates in the face of reduced challenge.     

Role of environmental persistence in pathogen transmission: a mathematical modeling approach

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.     

Phenotypic evolution under gene-culture transmission in structured populations.

I consider a simple model for the evolution of a quantitative character is structured populations when an offspring's phenotype is determined partly by his or her genetic constitution and partly by cultural transmission of the parental phenotype. Analysis of the model indicates that when individual and group selection are in the same direction, phenotypic evolution always proceeds faster under gene-culture vs. purely genetic transmission. When individual and group selection are countervailing, altruistic characters evolve faster under gene-culture transmission when individual selection is weak and migration among groups is limited, with increased individual selection and migration tending to decrease the advantage of gene-culture transmission over purely genetic transmission. Given the prevalence of cultural transmission in higher species, these results suggest that contrary to what is often assumed, group selection may indeed by a potent evolutionary force in the evolution of altruistic characters.     

The zoonotic transmission of Giardia and Cryptosporidium

The molecular characterisation of Giardia and Cryptosporidium has given rise to a more epidemiological meaningful and robust taxonomy. Importantly, molecular tools are now available for 'typing' isolates of the parasites directly from clinical and environmental samples. As a consequence, information on zoonotic potential has been obtained although the frequency of zoonotic transmission is still poorly understood. Analysis of outbreaks and case-control studies, especially when coupled with genotyping data, is slowly providing information on the public health significance of zoonotic transmission. Such studies support the hypothesis that Cryptosporidium hominis is spread only between humans but that the major reservoir for Cryptosporidium parvum is domestic livestock, predominantly cattle, and that direct contact with infected cattle is a major transmission pathway along with indirect transmission through drinking water. The situation is less clearcut for Giardia duodenalis but the evidence does not, in general, support zoonotic transmission as a major risk for human infections. However, for both parasites there is a need for molecular epidemiological studies to be undertaken in well-defined foci of transmission in order to fully determine the frequency and importance of zoonotic transmission.     

The curse of the Pharaoh revisited: evolutionary bi-stability in environmentally transmitted pathogens

It is increasingly evident that for a number of high-profile pathogens, transmission involves both direct and environmental pathways. Much of the distinguished evolutionary theory has, however, focused on each of transmission component separately. Herein, we use the framework of adaptive dynamics to study the evolutionary consequences of mixed transmission. We find that environmental transmission can select for increased virulence when direct transmission is low. Increasing the efficiency of direct transmission gives rise to an evolutionary bi-stability, with coexistence of different levels of virulence. We conclude that the overlooked contribution of environmental transmission may explain the curious appearance of high virulence in pathogens that are typically only moderately pathogenic, as observed for avian influenza viruses and cholera.     

Theoretical aspects of the mode of transmission in cultural inheritance.

This study investigates how evolutionary factors interact to determine the relative importance of vertical versus nonvertical mode of transmission in cultural inheritance. Simple mathematical models are provided to study the joint evolution of two cultural characters, one determining the viability and the fertility of individuals, and the other determining the vertical transmission rate of the first trait. Ordinary local stability analyses indicate that intrademic processes should lead to a greater reliance on vertical cultural transmission. On the other hand, when newly arisen variants are adaptive and favored in biased cultural transmission, interdemic processes may lead to a decrease in vertical transmission. This is because biased nonvertical transmission may effectively propagate the adaptive variants, further increasing the average growth rate of the population. These results are verified under several distinct sets of assumptions. It is also inferred that the degree and intensity of transmission bias may be the important determinants of cultural processes.