Control of transmission with two types of infection

The effectiveness of a vaccination strategy to control transmission of an infectious disease depends on the way vaccine doses are distributed to individuals in a community of households. Here we show that this dependence is more complicated when acquisition and severity of illness are determined by the size of the infecting dose, as is thought to be the case for measles and varicella. Two alternative formulations for the way vaccination changes an individual's susceptibility and infectivity show that vaccination coverage, the nature of the vaccine response and the distribution of household size also have a big impact on which strategy is more effective. These judgements are made by comparing the post-vaccination reproduction numbers corresponding to different vaccination strategies.     

Seasonal Influenza Vaccination amongst Medical Students: A Social Network Analysis Based on a Cross-Sectional Study

Introduction

The Chief Medical Officer for England recommends that healthcare workers have a seasonal influenza vaccination in an attempt to protect both patients and NHS staff. Despite this, many healthcare workers do not have a seasonal influenza vaccination. Social network analysis is a well-established research approach that looks at individuals in the context of their social connections. We examine the effects of social networks on influenza vaccination decision and disease dynamics.

Methods

We used a social network analysis approach to look at vaccination distribution within the network of the Lancaster Medical School students and combined these data with the students’ beliefs about vaccination behaviours. We then developed a model which simulated influenza outbreaks to study the effects of preferentially vaccinating individuals within this network.

Results

Of the 253 eligible students, 217 (86%) provided relational data, and 65% of responders had received a seasonal influenza vaccination. Students who were vaccinated were more likely to think other medical students were vaccinated. However, there was no clustering of vaccinated individuals within the medical student social network. The influenza simulation model demonstrated that vaccination of well-connected individuals may have a disproportional effect on disease dynamics.

Conclusions

This medical student population exhibited vaccination coverage levels similar to those seen in other healthcare groups but below recommendations. However, in this population, a lack of vaccination clustering might provide natural protection from influenza outbreaks. An individual student’s perception of the vaccination coverage amongst their peers appears to correlate with their own decision to vaccinate, but the directionality of this relationship is not clear. When looking at the spread of disease within a population it is important to include social structures alongside vaccination data. Social networks influence disease epidemiology and vaccination campaigns designed with information from social networks could be a future target for policy makers.     

Imperfect vaccine aggravates the long-standing dilemma of voluntary vaccination

Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects individuals' vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effective game theoretic model of vaccination behavior with an epidemiological process. Our analysis shows that, in a population of self-interested individuals, there exists an overshooting of vaccine uptake levels as the effectiveness of vaccination increases. Moreover, when the basic reproductive number, R0, exceeds a certain threshold, all individuals opt for vaccination for an intermediate region of vaccine efficacy. We further show that increasing effectiveness of vaccination always increases the number of effectively vaccinated individuals and therefore attenuates the epidemic strain. The results suggest that 'number is traded for efficiency': although increases in vaccination effectiveness lead to uptake drops due to free-riding effects, the impact of the epidemic can be better mitigated.     

Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis

The aim of this paper is to study the impact of introducing a partially protective vaccine on the dynamics of infection in SIRS models where primary and secondary infections are distinguished. We investigate whether a public health strategy based solely on vaccinating a proportion of newborns can lead to an effective control of the disease. In addition to carrying out the qualitative analysis, the findings are further explained by numerical simulations. The model exhibits backward bifurcation for certain values of the parameters. In these cases the standard basic reproduction number (obtained by inspection of the uninfected state) is not significant. The key threshold is the reinfection level which depends on the relative transmissibility (susceptibility) of secondary, with respect to primary, infected (susceptible) individuals and the relative loss of immunity of vaccinated, with respect to recovered, individuals. If one or all of these ratios decrease, then the threshold increases which increases the possibility to contain the infection by vaccination. The analysis shows further that symptomatic infections can be eliminated by vaccination solely.     

Modelling infectious diseases with relapse: a case study of HSV-2

Background

Herpes Simplex Virus Type 2 (HSV-2) is one of the most common sexually transmitted diseases. Although there is still no licensed vaccine for HSV-2, a theoretical investigation of the potential effects of a vaccine is considered important and has recently been conducted by several researchers. Although compartmental mathematical models were considered for each special case in the previous studies, as yet there are few global stability results.

Results

In this paper, we formulate a multi-group SVIRI epidemic model for HSV-2, which enables us to consider the effects of vaccination, of waning vaccine immunity, and of infection relapse. Since the number of groups is arbitrary, our model can be applied to various structures such as risk, sex, and age group structures. For our model, we define the basic reproduction number ?₀ and prove that if ?₀≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if ?₀>1, then the endemic equilibrium is so. Based on this global stability result, we estimate ?₀ for HSV-2 by applying our model to the risk group structure and using US data from 2001 to 2014. Through sensitivity analysis, we find that ?₀ is approximately in the range of 2-3. Moreover, using the estimated parameters, we discuss the optimal vaccination strategy for the eradication of HSV-2.

Conclusions

Through discussion of the optimal vaccination strategy, we come to the following conclusions. (1) Improving vaccine efficacy is more effective than increasing the number of vaccines. (2) Although the transmission risk in female individuals is higher than that in male individuals, distributing the available vaccines almost equally between female and male individuals is more effective than concentrating them within the female population.

     

Evolution in metacommunities

A metacommunity can be defined as a set of communities that are linked by migration, and extinction and recolonization. In metacommunities, evolution can occur not only by processes that occur within communities such as drift and individual selection, but also by among-community processes, such as divergent selection owing to random differences among communities in species composition, and group and community-level selection. The effect of these among-community-level processes depends on the pattern of migration among communities. Migrating units may be individuals (migrant pool model), groups of individuals (single-species propagule pool model) or multi-species associations (multi-species propagule pool model). The most interesting case is the multi-species propagule pool model. Although this pattern of migration may a priori seem rare, it becomes more plausible in small well-defined 'communities' such as symbiotic associations between two or a few species. Theoretical models and experimental studies show that community selection is potentially an effective evolutionary force. Such evolution can occur either through genetic changes within species or through changes in the species composition of the communities. Although laboratory studies show that community selection can be important, little is known about how important it is in natural populations.     

Detecting Differential Transmissibilities That Affect the Size of Self-Limited Outbreaks

Our ability to respond appropriately to infectious diseases is enhanced by identifying differences in the potential for transmitting infection between individuals. Here, we identify epidemiological traits of self-limited infections (i.e. infections with an effective reproduction number satisfying ) that correlate with transmissibility. Our analysis is based on a branching process model that permits statistical comparison of both the strength and heterogeneity of transmission for two distinct types of cases. Our approach provides insight into a variety of scenarios, including the transmission of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the Arabian peninsula, measles in North America, pre-eradication smallpox in Europe, and human monkeypox in the Democratic Republic of the Congo. When applied to chain size data for MERS-CoV transmission before 2014, our method indicates that despite an apparent trend towards improved control, there is not enough statistical evidence to indicate that has declined with time. Meanwhile, chain size data for measles in the United States and Canada reveal statistically significant geographic variation in , suggesting that the timing and coverage of national vaccination programs, as well as contact tracing procedures, may shape the size distribution of observed infection clusters. Infection source data for smallpox suggests that primary cases transmitted more than secondary cases, and provides a quantitative assessment of the effectiveness of control interventions. Human monkeypox, on the other hand, does not show evidence of differential transmission between animals in contact with humans, primary cases, or secondary cases, which assuages the concern that social mixing can amplify transmission by secondary cases. Lastly, we evaluate surveillance requirements for detecting a change in the human-to-human transmission of monkeypox since the cessation of cross-protective smallpox vaccination. Our studies lay the foundation for future investigations regarding how infection source, vaccination status or other putative transmissibility traits may affect self-limited transmission.     

Estimating the immunity coverage required to prevent epidemics in a community of households

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.     

An Innovative Influenza Vaccination Policy: Targeting Last Season's Patients

Influenza vaccination is the primary approach to prevent influenza annually. WHO/CDC recommendations prioritize vaccinations mainly on the basis of age and co-morbidities, but have never considered influenza infection history of individuals for vaccination targeting. We evaluated such influenza vaccination policies through small-world contact networks simulations. Further, to verify our findings we analyzed, independently, large-scale empirical data of influenza diagnosis from the two largest Health Maintenance Organizations in Israel, together covering more than 74% of the Israeli population. These longitudinal individual-level data include about nine million cases of influenza diagnosed over a decade. Through contact network epidemiology simulations, we found that individuals previously infected with influenza have a disproportionate probability of being highly connected within networks and transmitting to others. Therefore, we showed that prioritizing those previously infected for vaccination would be more effective than a random vaccination policy in reducing infection. The effectiveness of such a policy is robust over a range of epidemiological assumptions, including cross-reactivity between influenza strains conferring partial protection as high as 55%. Empirically, our analysis of the medical records confirms that in every age group, case definition for influenza, clinical diagnosis, and year tested, patients infected in the year prior had a substantially higher risk of becoming infected in the subsequent year. Accordingly, considering individual infection history in targeting and promoting influenza vaccination is predicted to be a highly effective supplement to the current policy. Our approach can also be generalized for other infectious disease, computer viruses, or ecological networks.     

An integral equation model for the control of a smallpox outbreak

An integral equation model of a smallpox epidemic is proposed. The model structures the incidence of infection among the household, the workplace, the wider community and a health-care facility; and incorporates a finite incubation period and plausible infectivity functions. Linearisation of the model is appropriate for small epidemics, and enables analytic expressions to be derived for the basic reproduction number and the size of the epidemic. The effects of control interventions (vaccination, isolation, quarantine and public education) are explored for a smallpox epidemic following an imported case. It is found that the rapid identification and isolation of cases, the quarantine of affected households and a public education campaign to reduce contact would be capable of bringing an epidemic under control. This could be used in conjunction with the vaccination of healthcare workers and contacts. Our results suggest that prior mass vaccination would be an inefficient method of containing an outbreak.     

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.     

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.     

On vaccine efficacy and reproduction numbers

We consider the impact of a vaccination programme on the transmission potential of the infection in large populations. We define a measure of vaccine efficacy against transmission which combines the possibly random effect of the vaccine on individual susceptibility and infectiousness. This definition extends some previous work in this area to arbitrarily heterogeneous populations with one level of mixing, but leads us to question the usefulness of the concept of vaccine efficacy against infectiousness. We derive relationships between vaccine efficacy against transmission, vaccine coverage and reproduction numbers, which generalize existing results. In particular we show that the projected reproduction number RV does not depend on the details of the vaccine model, only on its overall effect on transmission. Explicit expressions for RV and the basic reproduction number R0 are obtained in a variety of settings. We define a measure of projected effectiveness of a vaccination programme PE=1-(RV/R0) and investigate its relationship with efficacy against transmission and vaccine coverage. We also study the effective reproduction number Re(t) at time t. Monitoring Re(t) over time is an important aspect of programme surveillance. Programme effectiveness PE is less sensitive than RV or the critical vaccination threshold to model assumptions. On the other hand Re(t) depends on the details of the vaccine model.     

Modeling the Population Level Effects of an HIV-1 Vaccine in an Era of Highly Active Antiretroviral Therapy

First generation HIV vaccines may have limited ability to prevent infection. Instead, they may delay the onset of AIDS or reduce the infectiousness of vaccinated individuals who become infected. To assess the population level effects of such a vaccine, we formulate a deterministic model for the spread of HIV in a homosexual population in which the use of highly active antiretroviral therapy (HAART) to treat HIV infection is incorporated. The basic reproduction number R ₀ is obtained under this model. We then expand the model to include the potential effects of a prophylactic HIV vaccine. The reproduction number R _f is derived for a population in which a fraction f of susceptible individuals is vaccinated and continues to benefit from vaccination. We define f ^* as the minimum vaccination fraction for which R _f ≤1 and describe situations in which it equals the critical vaccination fraction necessary to eliminate disease. When R ₀ is large or an HIV vaccine is only partially effective, the critical vaccination fraction may exceed one. HIV vaccination, however, may still reduce the prevalence of disease if the reduction in infectiousness is at least as great as the reduction in the rate of disease progression. In particular, a vaccine that reduces infectiousness during acute infection may have an important public health impact especially if coupled with counseling to reduce risky behavior.     

Estimating individual and household reproduction numbers in an emerging epidemic

Reproduction numbers, defined as averages of the number of people infected by a typical case, play a central role in tracking infectious disease outbreaks. The aim of this paper is to develop methods for estimating reproduction numbers which are simple enough that they could be applied with limited data or in real time during an outbreak. I present a new estimator for the individual reproduction number, which describes the state of the epidemic at a point in time rather than tracking individuals over time, and discuss some potential benefits. Then, to capture more of the detail that micro-simulations have shown is important in outbreak dynamics, I analyse a model of transmission within and between households, and develop a method to estimate the household reproduction number, defined as the number of households infected by each infected household. This method is validated by numerical simulations of the spread of influenza and measles using historical data, and estimates are obtained for would-be emerging epidemics of these viruses. I argue that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation.     

Plankton community structure in fluctuating environments and the role of productivity

Environmental variability in space and time can have significant influences on community structure. Temporal heterogeneity in nutrient supply has been shown in laboratory studies to have strong impacts on the diversity and composition of phytoplankton communities, depending on the scale of fluctuations. This paper extends the work in chemostats in a number of ways: using large-scale field mesocosms with natural plankton communities exposed to various frequencies of vertical mixing, modifying environmental productivity and incorporating higher trophic levels. The first major question and experiment focus on whether vertical mixing at various frequencies, and the associated nutrient pulse, has similar effects in nutrient-rich and nutrient-poor environments for predominantly single trophic level systems. The results indicate that the temporal scale of fluctuation is more of a structuring factor for phytoplankton communities in enriched enclosures, with little response under oligotrophic conditions. The second experiment examines the responsiveness of entire plankton communities (three trophic levels). Major shifts in community structure were absent under both nutrient-rich and nutrient-poor conditions. Responses were seen only in the demography of the top trophic level ( Chaoborus flavicans ). It appears from these experiments that the spatial disruption that accompanies mixing events may be more important than the temporal component (nutrient pulses) for phytoplankton. This appears to be the case only under conditions where natural spatial heterogeneity is high as it is when systems are enriched. When nutrient pulses are small, as they are in oligotrophic systems where recycling is efficient, little phytoplankton community response is observed. Finally, the inclusion of entire plankton food webs here suppressed the effects of the scale of intermittency in water column mixing at both low and high nutrient levels for all but the highest trophic level.     

The effect of structural behavior change on the spread of HIV in a one-sex population.

Within a preferred mixing type of model for the spread of HIV in a one-sex population, the effects of structural behavior change, that is movements of individuals from one activity class to another, with accompanying changes of contact pattern are investigated. It is concluded that such behavior change makes it more difficult for an epidemic to arise if the contact pattern is of the restricted type, whereas the effect is indeterminate in the proportional mixing case. Some of the problems in analyzing sexual activity data from a population within which this behavior change mechanism is at work are also commented upon.     

Assessing the potential impact of Salmonella vaccines in an endemically infected dairy herd

Salmonella spp. in cattle contribute to bacterial foodborne disease for humans. Reduction of Salmonella prevalence in herds is important to prevent human Salmonella infections. Typical control measures are culling of infectious animals, vaccination, and improved hygiene management. Vaccines have been developed for controlling Salmonella transmission in dairy herds; however, these vaccines are imperfect and a variety of vaccine effects on susceptibility, infectiousness, Salmonella shedding level, and duration of infectious period were reported. To assess the potential impact of imperfect Salmonella vaccines on prevalence over time and the eradication criterion, we developed a deterministic compartmental model with both replacement (cohort) and lifetime (continuous) vaccination strategies, and applied it to a Salmonella Cerro infection in a dairy farm. To understand the uncertainty of prevalence and identify key model parameters, global parameter uncertainty and sensitivity analyses were performed. The results show that imperfect Salmonella vaccines reduce the prevalence of Salmonella Cerro. Among three vaccine effects that were being considered, decreasing the length of the infectious period is most effective in reducing the endemic prevalence. Analyses of contour lines of prevalence or the critical reproduction ratio illustrate that, reducing prevalence to a certain level or zero can be achieved by choosing vaccines that have either a single vaccine effect at relatively high effectiveness, or two or more vaccine effects at relatively low effectiveness. Parameter sensitivity analysis suggests that effective control measures through applying Salmonella vaccines should be adjusted at different stages of infection. In addition, lifetime (continuous) vaccination is more effective than replacement (cohort) vaccination. The potential application of the developed vaccination model to other Salmonella serotypes related to foodborne diseases was also discussed. The presented study may be used as a tool for guiding the development of Salmonella vaccines.     

F-statistics under alternation of sexual and asexual reproduction: a model and data from schistosomes (platyhelminth parasites)

Accurate inferences on population genetics data require a sound underlying theoretical null model. Nearly nothing is known about the gene dynamics of organisms with complex life cycles precluding any biological interpretation of population genetics parameters. In this article, we used an infinite island model to derive the expectations of those parameters for the life cycle of a dioecious organism obligatorily alternating sexual and asexual reproductions as it is the case for schistosomes (plathyhelminth parasites). This model allowed us to investigate the effects of the degree of mixing among individuals coming from different subpopulations at each new generation (represented in the model by the migration rates before and after clonal reproductions) and the variance in the reproductive success of individuals during the clonal phase. We also consider the effects of different migration rates and degrees of clonal reproductive skew between male and female individuals. Results show that the variance in the reproductive success of clones is very important in shaping the distribution of the genetic variability both within and among subpopulations. Thus, higher variance in the reproductive success of clones generates heterozygous excesses within subpopulations and also increases genetic differentiation between them. Migration occurring before and after asexual reproduction has different effects on the patterns of F(IS) and F(ST). When males and females display different degrees of reproductive skew or migration rates, we observe differences in their respective population genetic structure. While results of the model apply to any organism alternating sexual and clonal reproductions (e.g. all parasitic trematodes, many plants, and all aphididae), we finally confront some of these theoretical expectations to empirical data from Schistosoma mansoni infecting Rattus rattus in Guadeloupe.