Implications of vaccination and waning immunity

Assessing vaccine efficacy for infectious diseases with variable immunity using a mathematical model

This study introduces an SIRS compartmental mathematical model encompassing vaccination and variable immunity periods for infectious diseases. I derive a basic reproduction number formula and assess the local and global stability of disease-free and the local stability of the endemic equilibria. I demonstrate that the basic reproduction number in the presence of a vaccine is highly sensitive to the rate of immunity loss, and even a slight reduction in this rate can significantly contribute to disease control. Additionally, I have derived a formula to calculate the critical efficacy period required for a vaccine to effectively manage and control the disease.The analysis conducted for the model suggests that increasing the vaccine's immunity duration (efficacy) decelerates disease dynamics, leading to reduced rates of reinfection and less severe disease outcomes. Furthermore, this delay contributes to a decrease in the basic reproduction number ( R 0 ), thus facilitating more rapid disease control efforts.

SIRS epidemics with individual heterogeneity of immunity waning

In the current paper we analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also includes vaccination schemes aimed to reach and maintain herd immunity. We consider both the informed situation where the individual waning parameters are known, thus allowing selection of vaccinees being based on both time since last vaccination as well as on the individual waning rate, and the more likely uninformed situation where individual waning parameters are unobserved, thus only allowing vaccination schemes to depend on time since last vaccination. The optimal vaccination policies for both the informed and uniformed heterogeneous situation are derived and compared with the homogeneous waning model (meaning all individuals have the same immunity waning rate), as well as to the classic SIRS model where immunity at the individual level drops from complete immunity to complete susceptibility in one leap. It is shown that the classic SIRS model requires least vaccines, followed by the SIRS with homogeneous gradual waning, followed by the informed situation for the model with heterogeneous gradual waning. The situation requiring most vaccines for herd immunity is the most likely scenario, that immunity wanes gradually with unobserved individual heterogeneity. For parameter values chosen to mimic COVID-19 and assuming perfect initial immunity and cumulative immunity of 12 months, the classic homogeneous SIRS epidemic suggests that vaccinating individuals every 15 months is sufficient to reach and maintain herd immunity, whereas the uninformed case for exponential waning with rate heterogeneity corresponding to a coefficient of variation being 0.5, requires that individuals instead need to be vaccinated every 4.4 months.

Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual, continued persistence of the pathogen within the population requires the replenishment of susceptibles through births, immigration, or waning immunity. Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection. If, initially, the prevalence of disease increases (that is, the infection takes off), the number of infectives will usually decrease to a low level after the first major outbreak. During this post-outbreak period, the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. Die out in this period following the first major outbreak is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start. In this study, we investigate if the rate of waning immunity (and other epidemiological parameters) can be reliably estimated from multiple outbreak data, in which some outbreaks display epidemic fade-out and others do not. We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities. Some outbreaks faded-out and some did not. We conducted Bayesian parameter estimation under two alternative approaches: independently on each outbreak and under a hierarchical framework. When conducting independent estimation, the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed. However, under a hierarchical approach, we obtained more accurate and precise posterior estimates for the rate of waning immunity and other epidemiological parameters. The greatest improvement in estimates was obtained for those communities in which epidemic fade-out was observed. Our findings demonstrate the feasibility and value of adopting a Bayesian hierarchical approach for parameter inference for stochastic epidemic models.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Buccopharyngeal route administered high polyphenolic olive oil and COVID-19: A pilot clinical trial

INTRODUCTION

Waning immunity after vaccination justifies the need for additional effective COVID-19 treatments. Immunomodulation of local immune response at the oropharyngeal mucosa could hypothetically activate mucosal immunity, which can prevent SARS-CoV-2 main immune evasion mechanisms in early stages of the disease and send an effective warning to other components of immune system. Olive polyphenols are biologically active compounds with immunomodulatory activity. There are previous studies based on immunomodulation with olive polyphenols and respiratory infections using an enteral route, which point to potential effects on time to resolution of symptoms. The investigators sought to determine whether participants following immunomodulation with tiny quantities of high polyphenolic olive oil administered through an oromucosal route could have a better outcome in COVID-19.

SUMMARY

This pilot clinical trial investigated the effect of buccopharyngeal administered high polyphenolic olive oil on COVID-19 incidence, duration, and severity.

IMPORTANCE

Waning immunity after vaccination justifies the need of further research for additional effective treatments for COVID-19.

OBJECTIVE

Immunomodulation of local immune response at the buccopharyngeal mucosa could hypothetically activate mucosal immunity, which would in turn difficult SARS-CoV-2 immune evasion mechanisms in early stages of the disease and send an effective warning to other components of immune system. Olive polyphenols are biologically active compounds with immunomodulatory activity. There are previous studies based on immunomodulation with olive polyphenols and respiratory infections, using an enteral route, which suggest potential shortening of time to resolution of symptoms. The investigators sought to determine whether participants following immunomodulation with tiny quantities of high polyphenolic olive oil administered through an oromucosal route could have a better outcome in COVID-19.

DESIGN, SETTING, AND PARTICIPANTS

Double blind, randomized pilot clinical trial conducted at a single site, Talavera de la Reina, Spain. Potential study participants were identified by simple random sampling from the epidemiological database of contact patients recently diagnosed of COVID-19 during the study period. A total of 88 adult participants were enrolled and 84 completed the 3-month study, conducted between July 1, 2021 and August 31, 2022.

INTERVENTION

Participants were randomized to receive oromucosal administered high polyphenolic olive oil, 2 mL twice a day for 3 months or no treatment.

MAIN OUTCOME AND MEASURES

Primary outcomes were incidence, duration, and severity of COVID-19 after intervention.

RESULTS

There were no differences in incidence between both groups but there were significant differences in duration, the median time to resolution of symptoms was 3 days in the high polyphenolic olive oil group compared with 7 days in the no-treatment group. Although time to resolution is directly related to severity, this study did not find any differences in severity.

CONCLUSION AND RELEVANCE

Among full-vaccinated adults recent infected with COVID-19, a daily intake of tiny quantities of oromucosal administered high polyphenolic olive oil before infection significantly improved the time to symptom resolution. This finding strongly support the appropriateness of further deep research on the use of oromucosal administered high polyphenolic olive oil as an effective immune strategy against COVID-19.

A perturbative approach to the analysis of many-compartment models characterized by the presence of waning immunity

The waning of immunity after recovery or vaccination is a major factor accounting for the severity and prolonged duration of an array of epidemics, ranging from COVID-19 to diphtheria and pertussis. To study the effectiveness of different immunity level-based vaccination schemes in mitigating the impact of waning immunity, we construct epidemiological models that mimic the latter's effect. The total susceptible population is divided into an arbitrarily large number of discrete compartments with varying levels of disease immunity. We then vaccinate various compartments within this framework, comparing the value of [Formula: see text] and the equilibria locations for our systems to determine an optimal immunization scheme under natural constraints. Relying on perturbative analysis, we establish a number of results concerning the location, existence, and uniqueness of the system's endemic equilibria, as well as results on disease-free equilibria. We use numerical techniques to supplement our analytical ones, applying our model to waning immunity dynamics in pertussis, among other diseases. Our analytical results are applicable to a wide range of systems composed of arbitrarily many ODEs.

Duration of humoral immunity from smallpox vaccination and its cross-reaction with Mpox virus

The ongoing pandemic caused by mpox virus (MPXV) has become an international public health emergency that poses a significant threat to global health. The vaccinia virus Tiantan strain (VTT) was used to vaccinate against smallpox in China 42 years ago. It is urgent to assess the level of immunity to smallpox in individuals vaccinated 43 or more years ago and evaluate their immunological susceptibility to MPXV. Here, we recruited 294 volunteers and detected the level of residual humoral immunity, including the vaccinia-specific IgG level and neutralizing antibody titer, and the cross-antibodies of MPXV A29L, B6R, A35R, and M1R. Our results showed that the humoral immunity from the smallpox vaccine in the population still remains, and VTT-specific NAb levels wane with age. The majority of the population pre-1981 who should be immunized with VTT still maintains certain levels of MPXV-specific antibodies, in particular, targeting A35R and B6R antigens. Furthermore, we separately analyzed the correlations between the OD450 values of VTT-specific IgG and A35R-specific IgG, B6R-specific IgG, and A29L-specific IgG with plasma samples diluted 1:40, showing a linear correlation (p < 0.0001). Our findings suggest that most Chinese populations still maintain VTT-specific IgG antibodies for 42 or more years after smallpox vaccination and could provide some level of protection against MPXV.

Extending susceptible-infectious-recovered-susceptible epidemics to allow for gradual waning of immunity

Susceptible-infectious-recovered-susceptible (SIRS) epidemic models assume that individual immunity wanes in one leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that has become even more evident during COVID-19 pandemic where also recently infected have a reinfection risk, and booster vaccines are given to increase immunity. Here, a novel mathematical model is presented allowing for the gradual decay of immunity following linear or exponential waning functions. The two new models and the SIRS model are compared assuming all three models have the same cumulative immunity. When no intervention is put in place, we find that the long-term prevalence is higher for the models with gradual waning. If aiming for herd immunity by continuous vaccination, it is shown that larger vaccine quantities are required when immunity wanes gradually compared with results obtained from the SIRS model, and this difference is the biggest for the most realistic assumption of exponentially waning of immunity. For parameter choices fitting to COVID-19, the critical amount of vaccine supply is about 50% higher if immunity wanes linearly, and more than 150% higher when immunity wanes exponentially, when compared with the classic SIRS epidemic model.

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

The effect of competition between health opinions on epidemic dynamics

Past major epidemic events showed that when an infectious disease is perceived to cause severe health outcomes, individuals modify health behavior affecting epidemic dynamics. To investigate the effect of this feedback relationship on epidemic dynamics, we developed a compartmental model that couples a disease spread framework with competition of two mutually exclusive health opinions (health-positive and health-neutral) associated with different health behaviors. The model is based on the assumption that individuals switch health opinions as a result of exposure to opinions of others through interpersonal communications. To model opinion switch rates, we considered a family of functions and identified the ones that allow health opinions to coexist. Finally, the model includes assortative mixing by opinions. In the disease-free population, either the opinions cannot coexist and one of them is always dominating (mono-opinion equilibrium) or there is at least one stable coexistence of opinions equilibrium. In the latter case, there is multistability between the coexistence equilibrium and the two mono-opinion equilibria. When two opinions coexist, it depends on their distribution whether the infection can invade. If presence of the infection leads to increased switching to a health-positive opinion, the epidemic burden becomes smaller than indicated by the basic reproduction number. Additionally, a feedback between epidemic dynamics and health opinion dynamics may result in (sustained) oscillatory dynamics and a switch to a different stable opinion distribution. Our model captures feedback between spread of awareness through social interactions and infection dynamics and can serve as a basis for more elaborate individual-based models.

Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity

This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection.

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Modeling the COVID-19 pandemic: a primer and overview of mathematical epidemiology

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape. From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Evaluating strategies for spatial allocation of vaccines based on risk and centrality

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritize some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritization include strategies that target those regions most at risk of importing the pathogen, and strategies that target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network and vaccine availability. We conclude that when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

A study on seroconversion following first & second doses of ChAdOx1 nCoV-19 vaccine in Central Kerala

Background & objectives

Vaccination against COVID-19 induces spike protein-binding IgG antibodies, a robust correlate of protection against COVID-19. This study was undertaken to assess the humoral response after completion of both the doses of ChAdOx1 nCoV vaccine in healthcare workers (HCWs) at a tertiary care health centre in India.

Methods

A cross-sectional COVID-19 vaccine-induced antibody study was conducted among HCWs. IgG antibodies against spike protein were measured at least 28 days after the first dose and the second dose of vaccination in both SARS CoV-2 naïve and recovered HCWs. Mean and median antibody titre following each dose of vaccine and its association with age, gender, co-morbidities and factors such as exercise, stress and sleep deprivation were also explored.

Results

Among the 200 vaccine recipients, 91.5 per cent showed seroconversion after the first dose and 99.5 per cent after the second dose. The mean titre after the second dose was significantly higher when compared to the first dose (12.68±4.17 vs. 9.83±6.3, P=0.001). More than half (54%) had high antibody titre ≥12 S/Co (Signal/cut-off). Previous COVID-19 infection was the single most important factor influencing antibody production, where the mean titre just after a single dose [mean-17.81±5.94, median-20.5 (interquartile range [IQR]-3.7)] surpassed the titre after the second dose in SARS CoV-2 naïve individuals [mean-12.29±4.00, median-12.8 (IQR-3.7), P=0.001]. Furthermore, 28 per cent of vaccinees showed a reduction in titre after the second dose. The mean fall in titre was 2.25±1.40 and was more pronounced in males, the younger age group and those with previous COVID-19 infection.

Interpretation & conclusions

ChAdOx1 nCov-19 vaccine after two doses elicited an excellent immune response. However, greater immunogenicity after the first dose was seen among those with previous COVID-19 infection, even surpassing the titre achieved by the second dose of vaccine in SARS CoV-2 naïve recipients. A fall in antibody titre after the second dose is a matter of concern and requires further studies.

The Elevated Expressions of Anti-lipopolysaccharide Factors After Priming Stimulation Confer Lastingly Humoral Protection in Crab Eriocheir sinensis

Evidence of immune memory in invertebrates (immune priming) has accumulated in various organisms, and both cellular and humoral immune reactions are speculated to be involved in immune priming. However, there is a lack of understanding of the molecular mechanisms involved. In the present study, the protective effect of primed haemolymph was further validated by the increased survival rate of naïve crabs receiving a transfusion of primed haemolymph. By proteomic analysis, there were 474 proteins identified from the primed haemolymph, and most of them were functionally annotated in transport and metabolism classes. A total of 70 proteins were found to be differentially expressed in haemolymph at 12 hours and 7 days after priming stimulation with Aeromonas hydrophila, among which anti-lipopolysaccharide factor 1 (EsALF-1) and 3 (EsALF-3) were identified as the most significant (p < 0.05). After being challenged with A. hydrophila, EsALF-1 and EsALF-3 were highly expressed at both mRNA (in haemocytes) and protein (in haemolymph) levels compared with blank crabs, and the mRNA expressions of components in the EsTLR1-EsMyd88-EsPelle-EsALF pathway also increased significantly (p < 0.05). The EsALF-3 and EsMyd88 were even significantly higher expressed in response to the second A. hydrophila challenge, but their expressions all decreased (p < 0.05) when EsTLR1 was knocked down by RNAi. After the naïve crabs received an injection with the recombinant protein of EsALF-1 (rEsALF-1) or EsALF-3 (rEsALF-3), their survival rate increased significantly (p < 0.05) upon A. hydrophila stimulation. In contrast, the survival rate of the primed crabs reduced significantly (p < 0.05) after they received an injection with the antibody of EsALF-1 or EsALF-3. The enhanced expressions of EsALF-1 and EsALF-3 after A. hydrophilap riming stimulation could sustain for four weeks. All the results suggested that the EsTLR1-mediated productions of EsALF-1 and EsALF-3 in haemolymph played an indispensable role in the month-long humoral immune protection induced by A. hydrophila, which provides solid evidence of immune priming in crabs and a valuable reference for further understanding immune memory in invertebrates.

The Role of Risk Perception in Students' COVID-19 Vaccine Uptake: A Longitudinal Study

Since COVID-19 vaccine uptake was found to be especially low among young adults, the present study investigated COVID-19 risk perception as predictor of COVID-19 vaccination intention and actual COVID-19 vaccine uptake among this age group. More specifically, it was tested whether cognitive risk perception predicts vaccination uptake successively via affective risk perception and vaccination intention. In total, 680 students (65.9% female) between 17 and 28 years participated in this longitudinal online study. COVID-19 cognitive and affective risk perception, COVID-19 vaccination intention, and actual COVID-19 vaccine uptake were measured in t1: November/December 2020, t2: March 2021, and t3: June/July 2021, respectively. The mediation analysis revealed a significant indirect effect of perceived severity at t1 on vaccine uptake at t3 via worry at t1 and vaccination intention at t2. Stronger perceptions of perceived severity of COVID-19 were related to more worry about COVID-19, which led to a higher vaccination intention, which, in turn, increased the chance of COVID-19 vaccine uptake. To increase vaccine uptake among young adults it might be fruitful to emphasize the severity of COVID-19. However, one should take into account that tapping into fear works best when messages also include efficacy statements.

COVID-19 Seroprevalence in Canada Modelling Waning and Boosting COVID-19 Immunity in Canada a Canadian Immunization Research Network Study

COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the Canadian population. This is the first mathematical model to do so. We estimate that 60-80% of the Canadian population has some immunity to COVID-19 by late Summer 2021, depending on specific characteristics of the vaccine and the waning rate of immunity. Models results indicate that increased vaccination uptake in age groups 12-29, and booster doses in age group 50+ are needed to reduce the severity COVID-19 Fall 2021 resurgence.

Exploring the COVID-19 vaccine candidates against SARS-CoV-2 and its variants: where do we stand and where do we go?

As of September 2021, 117 COVID-19 vaccines are in clinical development, and 194 are in preclinical development as per the World Health Organization (WHO) published draft landscape. Among the 117 vaccines undergoing clinical trials, the major platforms include protein subunit; RNA; inactivated virus; viral vector, among others. So far, USFDA recognized to approve the Pfizer-BioNTech (Comirnaty) COVID-19 vaccine for its full use in individuals of 16 years of age and older. Though the approved vaccines are being manufactured at a tremendous pace, the wealthiest countries have about 28% of total vaccines despite possessing only 10.8% of the total world population, suggesting an inequity of vaccine distribution. The review comprehensively summarizes the history of vaccines, mainly focusing on vaccines for SARS-CoV-2. The review also connects relevant topics, including measurement of vaccines efficacy against SARS-CoV-2 and its variants, associated challenges, and limitations, as hurdles in global vaccination are also kept forth.

Silent SARS-CoV-2 Infections, Waning Immunity, Serology Testing, and COVID-19 Vaccination: A Perspective

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus causes a spectrum of clinical manifestations, ranging from asymptomatic to mild, moderate, or severe illness with multi-organ failure and death. Using a new machine learning algorithm developed by us, we have reported a significantly higher number of predicted COVID-19 cases than the documented counts across the world. The sole reliance on confirmed symptomatic cases overlooking the symptomless COVID-19 infections and the dynamics of waning immunity may not provide 'true' spectrum of infection proportion, a key element for an effective planning and implementation of protection and prevention strategies. We and others have previously shown that strategic orthogonal testing and leveraging systematic data-driven modeling approach to account for asymptomatics and waning cases may situationally have a compelling role in informing efficient vaccination strategies beyond prevalence reporting. However, currently Centers for Disease Control and Prevention (CDC) does not recommend serological testing either before or after vaccination to assess immune status. Given the 27% occurrence of breakthrough infections in fully vaccinated (FV) group with many being asymptomatics and still a larger fraction of the general mass remaining unvaccinated, the relaxed mask mandate and distancing by CDC can drive resurgence. Thus, we believe it is a key time to focus on asymptomatics (no symptoms) and oligosymptomatics (so mild that the symptoms remain unrecognized) as they can be silent reservoirs to propagate the infection. This perspective thus highlights the need for proactive efforts to reevaluate the current variables/strategies in accounting for symptomless and waning fractions.

Simulating influenza epidemics with waning vaccine immunity

Observational studies indicate that vaccine-induced immunity can decline over time. However, few researchers have incorporated this kind of waning effect into their virus spread models. In this study, we simulate an influenza epidemic that considers the effects of waning immunity by fitting epidemiological models to CDC secondary historical data aggregated on a weekly basis, and derive the transmission rates at which susceptible individuals become infected over the course of the influenza season. Using a system of differential equations, we define four groups of individuals in a population: susceptible, vaccinated, infected, and recovered. We show that a larger number of initially infected individuals might not only bring the influenza season to an end sooner but also reduce the epidemic size. Moreover, any influenza virus that entails a faster recovery rate does not necessarily lead to a smaller epidemic size. We illustrate how simulation helps in understanding the effects of influenza epidemiological model in the presence of waning influenza vaccine immunity.

An age-structured epidemic model with boosting and waning of immune status

In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status could be boosted if they have contact with infective agent. According to the idea of the Aron's malaria model, we incorporate a boosting mechanism expressed by reset of recovery-age (immunity clock) into the SIRS epidemic model. We established the mathematical well-posedness of our formulation and showed that the initial invasion condition and the endemicity can be characterized by the basic reproduction number $ R_0 $. Our focus is to investigate the condition to determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, because it is a crucial point for disease prevention strategy whether there exist subcritical endemic steady states. Based on a recent result by Martcheva and Inaba ^[1], we have determined the direction of bifurcation that endemic steady states bifurcate from the disease-free steady state when the basic reproduction number passes through the unity. Finally, we have given a necessary and sufficient condition for backward bifurcation to occur.

Immune amnesia induced by measles and its effects on concurrent epidemics

It has been recently discovered that the measles virus can damage pre-existing immunological memory, destroying B lymphocytes and reducing the diversity of non-specific B cells of the infected host. In particular, this implies that previously acquired immunization from vaccination or direct exposition to other pathogens could be partially erased in a phenomenon named ‘immune amnesia’, whose effects can become particularly worrisome given the actual rise of anti-vaccination movements. Here, we present the first attempt to incorporate immune amnesia into standard models of epidemic spreading by proposing a simple model for the spreading of two concurrent pathogens causing measles and another generic disease. Different analyses confirm that immune amnesia can have important consequences for epidemic spreading, significantly altering the vaccination coverage required to reach herd immunity. We also uncover the existence of novel propagating and endemic phases induced by immune amnesia. Finally, we discuss the meaning and consequences of our results and their relation with, e.g. immunization strategies, together with the possibility that explosive types of transitions may emerge, making immune-amnesia effects particularly dramatic. This work opens the door to further developments and analyses of immune-amnesia effects, contributing also to the theory of interacting epidemics on complex networks.

ROLE OF REPEAT INFECTION IN THE DYNAMICS OF A SIMPLE MODEL OF WANING AND BOOSTING IMMUNITY

Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which exhibits rich dynamical behavior including supercritical and subcritical Hopf bifurcations among other structures. Here, we extend the bifurcation analyses of the SIRWS model to examine the influence of all parameters on these bifurcation structures. We show that the bistable region, involving both a stable fixed point and a stable limit cycle, exists only for a small region of biologically realistic parameter space. Furthermore, we contrast the SIRWS model with a modified version, where immune boosting may involve the occurrence of a secondary infection. Analysis of this extended model shows that oscillations and bistability, as found in the SIRWS model, depend on strong assumptions about infectivity and recovery rate from secondary infection. Understanding the dynamics of models of waning and boosting immunity is important for accurately assessing epidemiological data.

Dynamics of epidemics: Impact of easing restrictions and control of infection spread

During an infectious disease outbreak, mathematical models and computational simulations are essential tools to characterize the epidemic dynamics and aid in design public health policies. Using these tools, we provide an overview of the possible scenarios for the COVID-19 pandemic in the phase of easing restrictions used to reopen the economy and society. To investigate the dynamics of this outbreak, we consider a deterministic compartmental model (SEIR model) with an additional parameter to simulate the restrictions. In general, as a consequence of easing restrictions, we obtain scenarios characterized by high spikes of infections indicating significant acceleration of the spreading disease. Finally, we show how such undesirable scenarios could be avoided by a control strategy of successive partial easing restrictions, namely, we tailor a successive sequence of the additional parameter to prevent spikes in phases of low rate of transmissibility.

Dynamic analysis of the role of innate immunity in SEIS epidemic model

Consideration of every important aspect while modeling a disease makes the model more precise and the disease eradication strategy more powerful. In the present paper, we analyze the importance of innate immunity on SEIS modeling. We propose an SEIS model with Holling type II and type III functions representing innate immunity. We find the existence and stability conditions for the equilibria. When innate immunity is in the form of Holling type II function, the disease-free equilibrium exists for reproduction number less than unity and is locally asymptotically stable, and supercritical transcritical (forward) as well as subcritical transcritical (backward) bifurcation may occur where the contact rate β = β ∗ acts as the bifurcation parameter. Hence, disease-free equilibrium need not be globally stable. For reproduction number greater than unity unique endemic equilibrium exists which is locally asymptotically stable. The global stability conditions for the same are deduced with the help of Lozinski i ˘ measure. When innate immunity is considered a Holling type III function, the disease-free equilibrium point exists for reproduction number less than unity and is locally as well as globally stable. The existence of either unique or multiple endemic equilibria is found when reproduction number is greater than unity, and there exists at least one locally asymptotically stable equilibrium point and bistability can also be encountered. The conditions for the existence of Andronov-Hopf bifurcation are deduced for both cases. Moreover, we observe that ignoring innate immunity annihilates the possibility of Andronov-Hopf bifurcation. Numerical simulation is performed to validate the mathematical findings. Comparing the obtained results to the case when innate immunity is ignored, it is deduced that ignoring it ends the possibility of backward bifurcation, Andronov-Hopf bifurcation as well as the existence of multiple equilibria, and it also leads to the prediction of higher infection than the actual which may deflect the accuracy of the model to a high extent. This would further lead to false predictions and inefficient disease control strategies which in turn would make disease eradication a difficult and more expensive task.

Dynamical analysis of SEIS model with nonlinear innate immunity and saturated treatment

In this paper, we develop an SEIS model with Holling type II function representing the innate immunity as well as the saturated treatment. We obtain the existence and stability criteria for the equilibrium points. We observe that when the reproduction number is less than unity, the disease-free equilibrium always exists and is locally asymptotically stable. The multiple endemic equilibrium points can exist independent of the basic reproduction number, and the system may experience bistability. We find that the system can encounter backward or forward bifurcation at R 0 = 1 , where the contact rate β = β 0 is the bifurcation parameter. Therefore, the disease-free equilibrium may not be globally stable. We deduce the criteria for the presence of Hopf bifurcation where the parameter γ = γ ∗ acts as the bifurcation parameter and the system is a neutrally stable center. We also observe with the aid of a numerical example that a slight perturbation disrupts the neutral stability and the trajectories become either converging or diverging from the equilibrium point. Numerical simulation is performed with the help of MATLAB to justify the findings. We study the effect of nonlinearity of immunity function and the treatment rate on the dynamics of the disease spread. We find that when both are linear, the reproduction number is the same, but the system has a unique endemic equilibrium point that exists for reproduction number greater than unity. We find that there is neither backward bifurcation nor Hopf bifurcation. We also observe that the saturation in treatment enlarges the domain of backward bifurcation making disease eradication an extremely difficult task. The endemic equilibria in the case of saturated treatment may exist far more to the left of the bifurcation parameter β = β 0 . Hence, the nonlinearity of immunity function and treatment function affects the dynamics of an SEIS model highly; therefore, one must be precautious to choose an appropriate function for both while modeling.

The honeymoon period after mass vaccination

Vaccination is an effective method to prevent individuals from contracting diseases like measles and the flu. Its success is clearly demonstrated by the large declines in the incidence of many diseases (e.g., childhood diseases like measles) after the start of mass vaccination programs. However, what happens after this drop in incidence can be complicated. It is known that some diseases exhibit "honeymoon periods" (long periods of temporary low disease incidence after start of mass vaccination). These periods end with a natural resurgence of the disease, which is not due to any change in the system. To study honeymoon periods, we used the compartmental model analyzed in [1] that can exhibit different types of vaccine failures: failure in degree (leakiness), in take (all-or-nothing) and in duration (waning of vaccine-derived immunity). We showed that traditional measures of transient dynamics in ecology may not distinguish between models with different honeymoon periods. We also provide a proof of global stability of the endemic equilibrium when the reproduction number (accounting for vaccination) is greater than one, and introduce a technical definition of the honeymoon period.

Ecological and Evolutionary Challenges for Wildlife Vaccination

Wildlife vaccination is of urgent interest to reduce disease-induced extinction and zoonotic spillover events. However, several challenges complicate its application to wildlife. For example, vaccines rarely provide perfect immunity. While some protection may seem better than none, imperfect vaccination can present epidemiological, ecological, and evolutionary challenges. While anti-infection and antitransmission vaccines reduce parasite transmission, antidisease vaccines may undermine herd immunity, select for increased virulence, or promote spillover. These imperfections interact with ecological and logistical constraints that are magnified in wildlife, such as poor control and substantial trait variation within and among species. Ultimately, we recommend approaches such as trait-based vaccination, modeling tools, and methods to assess community- and ecosystem-level vaccine safety to address these concerns and bolster wildlife vaccination campaigns.

Evidence for Residual Immunity to Smallpox After Vaccination and Implications for Re-emergence

INTRODUCTION

Smallpox has been eradicated but advances in synthetic biology have increased the risk of its re-emergence. Residual immunity in individuals who were previously vaccinated may mitigate the impact of an outbreak, but there is a high degree of uncertainty about the duration and degree of residual immunity. Both cell-mediated and humoral immunity are thought to be important but the exact mechanisms of protection are unclear. Guidelines usually suggest vaccine-induced immunity wanes to zero after 3-10 years post vaccination, whereas other estimates show long term immunity over decades.

MATERIALS AND METHODS

A systematic review of the literature was conducted to quantify the duration and extent of residual immunity to smallpox after vaccination.

RESULTS

Twenty-nine papers related to quantifying residual immunity to smallpox after vaccination were identified: neutralizing antibody levels were used as immune correlates of protection in 11/16 retrospective cross-sectional studies, 2/3 epidemiological studies, 6/7 prospective vaccine trials and 0/3 modeling studies. Duration of protection of >20 years was consistently shown in the 16 retrospective cross-sectional studies, while the lowest estimated duration of protection was 11.7 years among the modeling studies. Childhood vaccination conferred longer duration of protection than vaccination in adulthood, and multiple vaccinations did not appear to improve immunity.

CONCLUSIONS

Most studies suggest a longer duration of residual immunity (at least 20 years) than assumed in smallpox guidelines. Estimates from modeling studies were less but still greater than the 3-10 years suggested by the WHO Committee on International Quarantine or US CDC guidelines. These recommendations were probably based on observations and studies conducted while smallpox was endemic. The cut-off values for pre-existing antibody levels of >1:20 and >1:32 reported during the period of endemic smallpox circulation may not be relevant to the contemporary population, but have been used as a threshold for identifying people with residual immunity in post-eradication era studies. Of the total antibodies produced in response to smallpox vaccination, neutralizing antibodies have shown to contribute significantly to immunological memory. Although the mechanism of immunological memory and boosting is unclear, revaccination is likely to result in a more robust response. There is a need to improve the evidence base for estimates on residual immunity to better inform planning and preparedness for re-emergent smallpox.

Waning immunity and re-emergence of measles and mumps in the vaccine era

Vaccine-preventable diseases (VPD) including measles and mumps have been re-emerging in countries with sustained high vaccine coverage. For mumps, waning immunity has been recognized as a major contributor to recent outbreaks. Although unvaccinated individuals account for most cases in recent measles outbreaks, the role of immune waning remains unclear. Accumulating serological and epidemiological evidence suggests that natural immunity induced by infection may be more durable compared to vaccine-induced immunity. As the proportion of population immunity via vaccination gradually increases and boosting through natural exposures becomes rare, risk of outbreaks may increase. Mechanistic insights into the coupled immuno-epidemiological dynamics of waning and boosting will be important to understand optimal vaccination strategies to combat VPD re-emergence and achieve eradication.

Integrating mathematical models with experimental data to investigate the within-host dynamics of bacterial infections

Bacterial infections still constitute a major cause of mortality and morbidity worldwide. The unavailability of therapeutics, antimicrobial resistance and the chronicity of infections due to incomplete clearance contribute to this phenomenon. Despite the progress in antimicrobial and vaccine development, knowledge about the effect that therapeutics have on the host–bacteria interactions remains incomplete. Insights into the characteristics of bacterial colonization and migration between tissues and the relationship between replication and host- or therapeutically induced killing can enable efficient design of treatment approaches. Recently, innovative experimental techniques have generated data enabling the qualitative characterization of aspects of bacterial dynamics. Here, we argue that mathematical modeling as an adjunct to experimental data can enrich the biological insight that these data provide. However, due to limited interdisciplinary training, efforts to combine the two remain limited. To promote this dialogue, we provide a categorization of modeling approaches highlighting their relationship to data generated by a range of experimental techniques in the area of in vivo bacterial dynamics. We outline common biological themes explored using mathematical models with case studies across all pathogen classes. Finally, this review advocates multidisciplinary integration to improve our mechanistic understanding of bacterial infections and guide the use of existing or new therapies.

How mechanistic modelling supports decision making for the control of enzootic infectious diseases

Controlling enzootic diseases, which generate a large cumulative burden and are often unregulated, is needed for sustainable farming, competitive agri-food chains, and veterinary public health. We discuss the benefits and challenges of mechanistic epidemiological modelling for livestock enzootics, with particular emphasis on the need for interdisciplinary approaches. We focus on issues arising when modelling pathogen spread at various scales (from farm to the region) to better assess disease control and propose targeted options. We discuss in particular the inclusion of farmers' strategic decision-making, the integration of within-host scale to refine intervention targeting, and the need to ground models on data.

Serological Immunity to Smallpox in New South Wales, Australia

The re-emergence of smallpox is an increasing and legitimate concern due to advances in synthetic biology. Vaccination programs against smallpox using the vaccinia virus vaccine ceased with the eradication of smallpox and, unlike many other countries, Australia did not use mass vaccinations. However, vaccinated migrants contribute to population immunity. Testing for vaccinia antibodies is not routinely performed in Australia, and few opportunities exist to estimate the level of residual population immunity against smallpox. Serological data on population immunity in Australia could inform management plans against a smallpox outbreak. Vaccinia antibodies were measured in 2003 in regular plasmapheresis donors at the Australian Red Cross Blood Service from New South Wales (NSW). The data were analysed to estimate the proportion of Australians in NSW with detectable serological immunity to vaccinia. The primary object of this study was to measure neutralising antibody titres against vaccinia virus. Titre levels in donor samples were determined by plaque reduction assay. To estimate current levels of immunity to smallpox infection, the decline in geometric mean titres (GMT) over time was projected using two values for the antibody levels estimated on the basis of different times since vaccination. The results of this study suggest that there is minimal residual immunity to the vaccinia virus in the Australian population. Although humoral immunity is protective against orthopoxvirus infections, cell-mediated immunity and immunological memory likely also play roles, which are not quantified by antibody levels. These data provide an immunological snapshot of the NSW population, which could inform emergency preparedness planning and outbreak control, especially concerning the stockpiling of vaccinia vaccine.

Modeling the waning and boosting of immunity from infection or vaccination

Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. We also model age, which affects contact, vaccination and possibly waning rates. The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 2007 and 2014, respectively. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective.

Host exposure history modulates the within-host advantage of virulence in a songbird-bacterium system

The host immune response can exert strong selective pressure on pathogen virulence, particularly when host protection against reinfection is incomplete. Since emerging in house finch populations, the bacterial pathogen Mycoplasma gallisepticum (MG) has been increasing in virulence. Repeated exposure to low-doses of MG, a proxy for what birds likely experience while foraging, provides significant but incomplete protection against reinfection. Here we sought to determine if the within-host, pathogen load advantage of high virulence is mediated by the degree of prior pathogen exposure, and thus the extent of immune memory. We created variation in host immunity by experimentally inoculating wild-caught, MG-naïve house finches with varying doses and number of exposures of a single pathogen strain of intermediate virulence. Following recovery from priming exposures, individuals were challenged with one of three MG strains of distinct virulence. We found that the quantitative pathogen load advantage of high virulence was strongly mediated by the degree of prior exposure. The greatest within-host load advantage of virulence was seen in hosts given low-dose priming exposures, akin to what many house finches likely experience while foraging. Our results show that incomplete host immunity produced by low-level prior exposure can create a within-host environment that favors more virulent pathogens.

The Use of Analgesics during Vaccination with a Live Attenuated Yersinia pestis Vaccine Alters the Resulting Immune Response in Mice

The administration of antipyretic analgesics prior to, in conjunction with, or due to sequelae associated with vaccination is a common yet somewhat controversial practice. In the context of human vaccination, it is unclear if even short-term analgesic regimens can significantly alter the resulting immune response, as literature exists to support several scenarios including substantial immune interference. In this report, we used a live attenuated Yersinia pestis vaccine to examine the impact of analgesic administration on the immune response elicited by a single dose of a live bacterial vaccine in mice. Mice were assessed by evaluating natural and provoked behavior, as well as food and water consumption. The resulting immune responses were assessed by determining antibody titers against multiple antigens and assaying cellular responses in stimulated splenocytes collected from vaccinated animals. We observed no substantial benefit to the mice associated with the analgesic administration. Splenocytes from both C57BL/6 and BALB/c vaccinated mice receiving acetaminophen have a significantly reduced interferon-gamma (IFN-γ) recall response. Additionally, there is a significantly lower immunoglobulin (Ig)G2a/IgG1 ratio in vaccinated BALB/c mice treated with either acetaminophen or meloxicam and a significantly lower IgG2c/IgG1 ratio in vaccinated C57BL/6 mice treated with acetaminophen. Taken together, our data indicate that the use of analgesics, while possibly ethically warranted, may hinder the accurate characterization and evaluation of novel vaccine strategies with little to no appreciable benefits to the vaccinated mice.

Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes. Consequently, the between-host system has two bifurcations determined by the corresponding basic reproduction number of the within-host and the size of the infected population at the interior equilibrium point. Analysis on the second model (Ebola infection) reveals the limited transient inhibitory effect of antibodies on viral replication, which influences the time window from infection to a potential outbreak. Simulations numerically illustrate our results.

An age-structured epidemic model with waning immunity and general nonlinear incidence rate

In this paper, a susceptible-vaccinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fluctuation lemma and the approach of Lyapunov functionals, we establish a threshold dynamics completely determined by the basic reproduction number. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, and otherwise the endemic steady state is globally asymptotically stable.

Multiscale model within-host and between-host for viral infectious diseases

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

The potential impact of a prophylactic vaccine for Ebola in Sierra Leone

The 2014 outbreak of Ebola virus disease (EVD) in West Africa was multinational and of an unprecedented scale primarily affecting the countries of Guinea, Liberia, and Sierra Leone. One of the qualities that makes EVD of high public concern is its potential for extremely high mortality rates (up to 90%). A prophylactic vaccine for ebolavirus (rVSV-ZEBOV) has been developed, and clinical trials show near-perfect efficacy. We have developed an ordinary differential equations model that simulates an EVD epidemic and takes into account (1) transmission through contact with infectious EVD individuals and deceased EVD bodies, (2) the heterogeneity of the risk of becoming infected with EVD, and (3) the increased survival rate of infected EVD patients due to greater access to trained healthcare providers. Using fitted parameter values that closely simulate the dynamics of the 2014 outbreak in Sierra Leone, we utilize our model to predict the potential impact of a prophylactic vaccine for the ebolavirus using various vaccination strategies including ring vaccination. Our results show that an rVSV-ZEBOV vaccination coverage as low as 40% in the general population and 95% in healthcare workers will prevent another catastrophic outbreak like the 2014 outbreak from occurring.

Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

Vaccination programs for childhood diseases, such as measles, mumps and rubella have greatly contributed to decreasing the incidence and impact of those diseases. Nonetheless, despite long vaccination programmes across the world, mumps has not yet been eradicated in those countries: indeed, large outbreaks continue. For example, in Scotland large outbreaks occurred in 2004, 2005, and 2015, despite introducing the MMR (Measles-Mumps-Rubella) vaccine more than 20 years ago. There are indications that this vaccine-preventable disease is re-emerging in highly vaccinated populations. Here we investigate whether the resurgence of mumps is due to waning immunity, and further, could a booster dose be the solution to eradicate mumps or would it just extend the period of waning immunity? Using mathematical modeling we enhance a seasonally-structured disease model with four scenarios: no vaccination, vaccinated individuals protected for life, vaccinated individuals at risk of waning immunity, and introduction of measures to increase immunity (a third dose, or a better vaccine). The model is parameterised from observed clinical data in Scotland 2004–2015 and the literature. The results of the four scenarios are compared with observed clinical data 2004–2016. While the force of infection is relatively sensitive to the duration of immunity and the number of boosters undertaken, we conclude that periodic large outbreaks of mumps will be sustained for all except the second scenario. This suggests that the current protocol of two vaccinations is optimal in the sense that while there are periodic large outbreaks, the severity of cases in vaccinated individuals is less than in unvaccinated individuals, and the size of the outbreaks does not decrease sufficiently with a third booster to make economic sense. This recommendation relies on continuous efforts to maintain high levels of vaccination uptake.

Vaccine impact in homogeneous and age-structured models

A general model of an imperfect vaccine for a childhood disease is presented and the effects of different types of vaccine failure on transmission were investigated using models that consider both homogeneous and age-specific mixing. The models are extensions of the standard SEIR equations with an additional vaccinated component that allows for five different vaccine parameters: three types of vaccine failure in decreasing susceptibility to infection via failure in degree ("leakiness"), take ("all-or-nothingness") and duration (waning of vaccine-derived immunity); one parameter reflecting the relative reduction in infectiousness of vaccinated individuals who get infected; and one parameter that reflects the relative reduction in reporting probability of vaccinated individuals due to a possible reduction in severity of symptoms. Only the first four parameters affect disease transmission (as measured by the basic reproduction number). The reduction in transmission due to vaccination is different for age-structured models than for homogeneous models. Notably, if the vaccine exhibits waning protection this could be larger for an age-structured model with high contact rates between young children who are still protected by the vaccine and lower contact rates between adults for whom protection might have already waned. Analytic expressions for age-specific "vaccine impacts" were also derived. The overall vaccine impact is bounded between the age-specific impact for the oldest age class and that of the youngest age class.

Toward Standardizing a Lexicon of Infectious Disease Modeling Terms

Disease modeling is increasingly being used to evaluate the effect of health intervention strategies, particularly for infectious diseases. However, the utility and application of such models are hampered by the inconsistent use of infectious disease modeling terms between and within disciplines. We sought to standardize the lexicon of infectious disease modeling terms and develop a glossary of terms commonly used in describing models’ assumptions, parameters, variables, and outcomes. We combined a comprehensive literature review of relevant terms with an online forum discussion in a virtual community of practice, mod4PH (Modeling for Public Health). Using a convergent discussion process and consensus amongst the members of mod4PH, a glossary of terms was developed as an online resource. We anticipate that the glossary will improve inter- and intradisciplinary communication and will result in a greater uptake and understanding of disease modeling outcomes in heath policy decision-making. We highlight the role of the mod4PH community of practice and the methodologies used in this endeavor to link theory, policy, and practice in the public health domain.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Pertussis immunity and epidemiology: mode and duration of vaccine-induced immunity

The resurgence of pertussis in some countries that maintain high vaccination coverage has drawn attention to gaps in our understanding of the epidemiological effects of pertussis vaccines. In particular, major questions surround the nature, degree and durability of vaccine protection. To address these questions, we used mechanistic transmission models to examine regional time series incidence data from Italy in the period immediately following the introduction of acellular pertussis (aP) vaccine. Our results concur with recent animal-challenge experiments wherein infections in aP-vaccinated individuals proved as transmissible as those in naive individuals but much less symptomatic. On the other hand, the data provide evidence for vaccine-driven reduction in susceptibility, which we quantify via a synthetic measure of vaccine impact. As to the precise nature of vaccine failure, the data do not allow us to distinguish between leakiness and waning of vaccine immunity, or some combination of these. Across the range of well-supported models, the nature and duration of vaccine protection, the age profile of incidence and the range of projected epidemiological futures differ substantially, underscoring the importance of the remaining unknowns. We identify key data gaps: sources of data that can supply the information needed to eliminate these remaining uncertainties.

Opportunities and challenges of Integral Projection Models for modelling host-parasite dynamics

Epidemiological dynamics are shaped by and may in turn shape host demography. These feedbacks can result in hard to predict patterns of disease incidence. Mathematical models that integrate infection and demography are consequently a key tool for informing expectations for disease burden and identifying effective measures for control.

A major challenge is capturing the details of infection within individuals and quantifying their downstream impacts to understand population‐scale outcomes. For example, parasite loads and antibody titres may vary over the course of an infection and contribute to differences in transmission at the scale of the population. To date, to capture these subtleties, models have mostly relied on complex mechanistic frameworks, discrete categorization and/or agent‐based approaches.

Integral Projection Models (IPMs) allow variance in individual trajectories of quantitative traits and their population‐level outcomes to be captured in ways that directly reflect statistical models of trait–fate relationships. Given increasing data availability, and advances in modelling, there is considerable potential for extending this framework to traits of relevance for infectious disease dynamics.

Here, we provide an overview of host and parasite natural history contexts where IPMs could strengthen inference of population dynamics, with examples of host species ranging from mice to sheep to humans, and parasites ranging from viruses to worms. We discuss models of both parasite and host traits, provide two case studies and conclude by reviewing potential for both ecological and evolutionary research.