Pathogen adaptation under imperfect vaccination: implications for pertussis

Mass vaccination campaigns have drastically reduced the burden of infectious diseases. Unfortunately, in recent years several infectious diseases have re-emerged. Pertussis poses a well-known example. Inspired by pertussis, we study, by means of an epidemic model, the population and evolutionary dynamics of a pathogen population under the pressure of vaccination. A distinction is made between infection in immunologically naive individuals (primary infection) and infection in individuals whose immune system has been primed by vaccination or infection (secondary infection). The results show that (i) vaccination with an imperfect vaccine may not succeed in reducing the infection pressure if the transmissibility of secondary infections is higher than that of primary infections; (ii) pathogen strains that are able to evade the immunity induced by vaccination can only spread if escape mutants incur no or only a modest fitness cost and (iii) the direction of evolution depends crucially on the distribution of the different types of susceptibles in the population. We discuss the implications of these results for the design and use of vaccines that provide temporary immunity.     

Population dynamic interference among childhood diseases.

Epidemiologists usually study the interaction between a host population and one parasitic infection. However, different parasite species effectively compete, in an ecological sense, for the same finite group of susceptible hosts, so there may be an indirect effect on the population dynamics of one disease due to epidemics of another. In human populations, recovery from any serious infection is normally preceded by a period of convalescence, during which infected individuals stay at home and are effectively shielded from exposure to other infectious diseases. We present a model for the dynamics of two infectious diseases, incorporating a temporary removal of susceptibles. We use this model to explore population-level consequences of a temporary insusceptibility in childhood diseases, the dynamics of which are partly driven by differences in contact rates in and out of school terms. Significant population dynamic interference is predicted and cannot be dismissed in the limited case-study data available for measles and whooping cough in England before the vaccination era.     

Modeling the simple epidemic with deterministic differential equations and random initial conditions

In a simple epidemic the only transition in the population is from susceptible to infected and the total population size is fixed for all time. This paper investigates the effect of random initial conditions on the deterministic model for the simple epidemic. By assuming a Beta distribution on the initial proportion of susceptibles, we define a distribution that describes the proportion of susceptibles in a population at any time during an epidemic. The mean and variance for this distribution are derived as hypergeometric functions, and the behavior of these functions is investigated. Lastly, we define a distribution to describe the time until a given proportion of the population remains susceptible. A method for finding the quantiles of this distribution is developed and used to make confidence statements regarding the time until a given proportion of the population is susceptible.     

Branching process models for surveillance of infectious diseases controlled by mass vaccination

Mass vaccination programmes aim to maintain the effective reproduction number R of an infection below unity. We describe methods for monitoring the value of R using surveillance data. The models are based on branching processes in which R is identified with the offspring mean. We derive unconditional likelihoods for the offspring mean using data on outbreak size and outbreak duration. We also discuss Bayesian methods, implemented by Metropolis-Hastings sampling. We investigate by simulation the validity of the models with respect to depletion of susceptibles and under-ascertainment of cases. The methods are illustrated using surveillance data on measles in the USA.     

Implications of vaccination and waning immunity

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40–80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.     

Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young Females

Genital Herpes, which is caused by Herpes Simplex Virus-1 or -2 (HSV-1, -2, predominantly HSV-2) is a sexually transmitted infection (STI) that causes a chronic latent infection with outbreak episodes linked to transmission. Antiviral therapies are effective in reducing viral shedding during these episodes, but are ineffective as a whole since many outbreaks are asymptomatic or have mild symptoms. Thus, the development of a vaccine for genital herpes is needed to control this disease. The question of how to implement such a vaccine program is an important one, and may be similar to the vaccination program for Human Papilloma Virus (HPV) for young females. We have developed a mathematical model to describe the epidemiology of vaccination targeting young females against HSV-2. The model population is delineated with respect to age group, sexual activity and infection status including oral infection of HSV-1, which may affect vaccine efficacy. A threshold parameter , which determines the level of vaccine uptake needed to eradicate HSV-2, is found. Computer simulation shows that an adolescent-only vaccination program may be effective in eliminating HSV-2 disease, however, the success of extinction greatly depends on the level of vaccine uptake, the vaccine efficacy, the age of sexual maturity and safe sex practices. However, the time course of eradication would take many years. We also investigate the prevalence of infection in the total population and in women between 16–30 years of age before and after vaccination has been introduced, and show that the adolescent-only vaccination program can be effective in reducing disease prevalence in these populations depending on the level of vaccine uptake and vaccine efficacy. This will also result in a decrease of maternal-fetal transmission of HSV-2 infection. Another important, if commonsense, conclusion is that vaccination of some females reduces infection in men, which then reduces infection in women.     

Epidemic process of pertussis in Moscow

Materials reflecting the dynamics of pertussis morbidity during the period of 1958 - 2003 under the conditions of prolonged mass immunization of the child population with adsorbed DPT vaccine are presented. The planned vaccination of children led to the decrease of pertussis morbidity during the first 10 years, but groundless abstentions from vaccination during the 1980s - 1990s contributed to a sharp rise in morbidity among children of younger age groups. During the recent four years a rise in pertussis morbidity was registered in 2000 (71.79 per 100,000 of the population), followed by the most significant for the last 20 years drop in morbidity in 2002--down to 9.89. But in 2003 the growth of morbidity was again registered (38.67). Recently periodic rises and drops in morbidity occurred simultaneously with the increased coverage of children of younger age groups with vaccination. In recent years changes in the age structure of patients were observed: the specific proportion of school children increased (in 2003 morbidity rates in children aged 6 - 10 years were 288.6 - 270.7), simultaneously high morbidity among children aged up to one year (274.9) was registered. The specific proportion of pertussis-affected children aged above 7 years reached 65%. From the late 1990s until present in 87.1% of cases strains of serotype 1.0.3 prevailed in the population of B. pertussis strains. But in recent years the circulation of strains 1.2.3, spread in the prevaccination period and having toxicity similar to that of strains of serotype 1.0.3, while exceeding them in virulence, in sufficiently high proportion (7.0% in 2002) was noted. This was indicative of the possibility of the unfavorable development of the epidemic process of pertussis infection.     

Using empirical social contact data to model person to person infectious disease transmission: An illustration for varicella

With the aim to improve dynamic models for infections transmitted predominantly through non-sexual social contacts, we compared three popular model estimation methods in how well they fitted seroprevalence data and produced estimates for the basic reproduction number R₀ and the effective vaccination level required for elimination of varicella. For two of these methods, interactions between age groups were parameterized using empirical social contact data whereas for the third method we used the current standard approach of imposing a simplifying structure on the ‘Who Acquires Infection From Whom’ (WAIFW) matrix. The first method was based on solving a set of differential equations to obtain an equilibrium value of the proportion of susceptibles. The second method was based on finding a solution for the age-specific force of infection using the formula of the mass action principle by means of iteration. Both solutions were contrasted with observed age-specific seroprevalence data. The best fit of the WAIFW matrix was obtained with contacts involving touching, and lasting longer than 15 min per day. Plausible values for R₀ for varicella in Belgium ranged from 7.66 to 13.44. Both approaches based on empirical social contact data provided a better fit to seroprevalence data than the current standard approach.     

A game dynamic model for delayer strategies in vaccinating behaviour for pediatric infectious diseases

Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice—rather than accessibility—is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.     

四省观察点人群中血清乙型肝炎病毒表面抗原消长趋势调查

本文以前瞻性血清流行病学方法调查了人群中血清HBsAg消长趋势。观察了3 096名HBV易感者,其人年总感染率为7.0％;HBsAg人年阳转率为0.68％,两者之比为10.3:1.0。HBsAg阳转者中51.2％发生在0～3岁时期。调查了772例HBsAg携带者,其人年标化阴转率为2.01％,阴转者主要发生在10～29岁和50岁以上年龄组,占总阴转数的66.7％。以人群HBsAg阴转率加上因自然死亡而损失的HBsAg携带率和人群中HBsAg年增长率进行分析计算,得出HBsAg在观察点人群中的消长状况是呈上升趋势,即年增加率为0.370％,年减少率为0.264％。     

Measles: prospects of vaccine prophylaxis and decrease of morbidity in Moscow

The results of the prolonged epidemiological surveillance on measles in Moscow are presented. The detailed analysis of the influence of immunization on the level of measles morbidity has been made. Changes in the age structure of measles patients with an essential increase in the proportion of adolescents and adults due to mass vaccination of the child population are shown. High risk groups have been determined according to the data of serological screening and epidemiological surveillance. The prospects of the vaccinal prophylaxis of measles under present conditions, as the basic intervention for achieving sporadic level of morbidity in this infection and further eradication are evaluated.     

Simple Epidemic Models with Positive Latent Period

This paper deals with two types of simple epidemic models, namely, deterministic and stochastic wherein the latent period is assumed to be positive. In the deterministic epidemic model, the distributions of susceptibles, inactive infectives, active infectives and that of epidemic curve which gives the rate at which new infections take place have been obtained. The expression for the expected time of the entire epidemic has been derived. Also the partial differential equation for the moment generating function of the proportion of susceptibles in the population is established. In the end, we have studied a stochastic approach of the system.     

Modeling malaria vaccines. II: Population effects of stage-specific malaria vaccines dependent on natural boosting

Population effects of malaria vaccination programs will depend on the stage specificity of the vaccine, its duration of effectiveness, whether it is responsive to natural boosting, the proportion vaccinated, and the preexisting endemic conditions. This paper develops models of infection-blocking (sporozoite), disease-modifying (merozoite), and transmission-blocking (gametic) vaccines. It explores numerically their different effects on prevalence of infection and disease when utilized in different types of immunization programs at various levels of coverage. Simulations show that possible qualitative consequences of malaria vaccination programs include decreased prevalence of infection and disease and decreased prevalence of infection without a corresponding decrease in prevalence of disease. Epidemics, either one-time or cyclical, could occur. These effects could be accompanied by changes in the age distribution of disease. Finally, vaccination could contribute to elimination of transmission. The duration of effectiveness of the malaria vaccine relative to the duration of natural immunity could have important consequences for the unvaccinated. The problem of predicting a threshold for elimination of transmission is discussed.     

Asymptotic behavior in a deterministic epidemic model

The effects of a periodic contact rate and of carriers are considered for a generalization of Bailey's simple epidemic model. In this model it is assumed that individuals become susceptible again as soon as they recover from the infection so that a fixed population can be divided into a class of infectives and a class of susceptibles which vary with time. If the contact rate is periodic, then the number of infectives as time approaches infinity either tends to zero or is asymptotically periodic depending on whether the total population size is less than or greater than a threshold value. The behavior for large time of the number of infectives is determined for three modifications of the model which involve carriers.     

The spatial spread and final size of models for the deterministic host-vector epidemic

A disease is considered which is transferred between two populations, termed hosts and vectors. The disease is transmitted solely from infected vector to uninfected host and from infected host to uninfected vector. Two models are formulated in which infectious individuals are introduced at time t = 0 into the populations of susceptibles, thus triggering an epidemic through those populations. Conditions are established for a major epidemic to occur, and the final size of the epidemic is obtained for these models when no spatial aspect is considered. When a spatial aspect is included in the models, again the condition for a major epidemic is obtained. The pandemic theorem is proved rigorously, giving a lower bound for the proportion of each population, at each point, who eventually suffer the epidemic. The behavior a long way from the initial focus of infection is also rigorously obtained.     

The segregation of lambs into ‘responders’ and ‘non-responders’: Response to vaccination with irradiated Trichostrongylus colubriformis larvae before weaning

Random bred Merino ram and ewe lambs were vaccinated at 1, 2 and/or 3 months of age with irradiated T. colubriformis larvae. An exponentially increasing challenge of normal larvae was given to all groups including unvaccinated controls commencing at 1 month of age. The results, based on faecal egg counts, showed a dissociation into animals which responded to vaccination (geometric mean egg count 441) and those which did not (geometric mean egg count 1567). The proportion of responders was greatest in groups first vaccinated at the earliest age (1 month). Wool growth and liveweight gains showed severe depression corresponding to peak egg counts, however, responders were less affected than non-responders. There was no correlation between haemoglobin type and resistance to challenge. Faecal egg counts after impulse challenge with 10,000 normal larvae given at about 6$\text{1}\text{2}$ months of age showed a significant ranked correlation with those obtained during the primary exponential challenge. These results confirm that a proportion of young lambs respond to vaccination with irradiated larvae, and that genetically-determined factors are implicated in the ability of animals to respond to vaccination at an early age.     

HPV Serology Testing Confirms High HPV Immunisation Coverage in England

Background

Reported human papillomavirus (HPV) vaccination coverage in England is high, particularly in girls offered routine immunisation at age 12 years. Serological surveillance can be used to validate reported coverage and explore variations within it and changes in serological markers over time.

Methods

Residual serum specimens collected from females aged 15–19 years in 2010–2011 were tested for anti-HPV16 and HPV18 IgG by ELISA. Based on these results, females were classified as follows: seronegative, probable natural infection, probable vaccine-induced seropositivity, or possible natural infection/possible vaccine-induced seropositivity. The proportion of females with vaccine-induced seropositivity was compared to the reported vaccination coverage.

Results

Of 2146 specimens tested, 1380 (64%) were seropositive for both types HPV16 and HPV18 and 159 (7.4%) positive for only one HPV type. The IgG concentrations were far higher for those positive for both HPV types than those positive for only one HPV type. 1320 (62%) females were considered to have probable vaccine-induced seropositivity. Among vaccine-induced seropositives, antibody concentrations declined with increasing age at vaccination and increasing time since vaccination.

Conclusions

The proportion of females with vaccine-induced seropositivity was closest to the reported 3-dose coverage in those offered the vaccination at younger ages, with a greater discrepancy in the older females. This suggests either some under-reporting of immunisations of older females and/or that partial vaccination (i.e. one- or two-doses) has provided high antibody responses in 13–17 year olds.     

Effect of selective vaccination on rubella susceptibility and infection in pregnancy.

The effect of school and adult vaccination on susceptibility to rubella in women of childbearing age was assessed in the Manchester area, where the population attending antenatal clinics is over 40 000 a year. Between 1979 and 1984 the proportion susceptible fell from 6.4% to 2.7%. In 1984, 4.2% of nulliparous women were susceptible compared with 1.4% of women in their second or subsequent pregnancy. Eighty five per cent of pregnant women screened and found to be non-immune were vaccinated post partum before leaving hospital. Requests for prevaccination screening of non-pregnant women increased in response to a national campaign and at the time of local outbreaks of rubella but only two thirds of those found to be nonimmune were subsequently vaccinated. During 1983 and 1984 infection was confirmed in 57 pregnant women--2% of those non-immune. Selective vaccination has reduced susceptibility to rubella in the childbearing population, but it is suggested that mass vaccination of children of both sexes should be added to the existing policy to control circulation of wild rubella virus and reduce the risk of infection to pregnant women who remain susceptible.