Investigating the impact of vaccine hesitancy on an emerging infectious disease: a mathematical and numerical analysis.

Throughout the last two centuries, vaccines have been helpful in mitigating numerous epidemic diseases. However, vaccine hesitancy has been identified as a substantial obstacle in healthcare management. We examined the epidemiological dynamics of an emerging infection under vaccination using an SVEIR model with differential morbidity. We mathematically analyzed the model, derived R0, and provided a complete analysis of the bifurcation at R0=1. Sensitivity analysis and numerical simulations were used to quantify the tradeoffs between vaccine efficacy and vaccine hesitancy on reducing the disease burden. Our results indicated that if the percentage of the population hesitant about taking the vaccine is 10%, then a vaccine with 94% efficacy is required to reduce the peak of infections by 40%. If 60% of the population is reluctant about being vaccinated, then even a perfect vaccine will not be able to reduce the peak of infections by 40%.

Key Factors and Parameter Ranges for Immune Control of Equine Infectious Anemia Virus Infection.

Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube sampling and least squares to find the parameter ranges that equally divide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.

Modelling Mutation in Equine Infectious Anemia Virus Infection Suggests a Path to Viral Clearance with Repeated Vaccination.

Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. The aim of this work is to determine whether repeated vaccinations through antibody infusions can reduce both the wild-type and mutant strains of the virus below one viral particle, and if so, to examine the vaccination period and number of infusions that ensure eradication. The antibody infusions are modelled using impulsive differential equations, a technique that offers insight into repeated vaccination by approximating the time-to-peak by an instantaneous change. We use impulsive theory to determine the maximal vaccination intervals that would be required to reduce the wild-type and mutant virus levels below one particle per horse. We show that seven boosts of the antibody vaccine are sufficient to eradicate both the wild-type and the mutant strains. In the case of a mutant virus infection that is given infusions of antibodies targeting wild-type virus (i.e., simulation of a heterologous infection), seven infusions were likewise sufficient to eradicate infection, based upon the data set. However, if the period between infusions was sufficiently increased, both the wild-type and mutant virus would eventually persist in the form of a periodic orbit. These results suggest a route forward to design antibody-based vaccine strategies to control viruses subject to mutant escape.

Ecological Approach to Understanding Superinfection Inhibition in Bacteriophage.

In microbial communities, viruses compete with each other for host cells to infect. As a consequence of competition for hosts, viruses evolve inhibitory mechanisms to suppress their competitors. One such mechanism is superinfection exclusion, in which a preexisting viral infection prevents a secondary infection. The bacteriophage ΦX174 exhibits a potential superinfection inhibition mechanism (in which secondary infections are either blocked or resisted) known as the reduction effect. In this auto-inhibitory phenomenon, a plasmid containing a fragment of the ΦX174 genome confers resistance to infection among cells that were once permissive to ΦX174. Taking advantage of this plasmid system, we examine the inhibitory properties of the ΦX174 reduction effect on a range of wild ΦX174-like phages. We then assess how closely the reduction effect in the plasmid system mimics natural superinfection inhibition by carrying out phage-phage competitions in continuous culture, and we evaluate whether the overall competitive advantage can be predicted by phage fitness or by a combination of fitness and reduction effect inhibition. Our results show that viral fitness often correctly predicts the winner. However, a phage's reduction sequence also provides an advantage to the phage in some cases, modulating phage-phage competition and allowing for persistence where competitive exclusion was expected. These findings provide strong evidence for more complex dynamics than were previously thought, in which the reduction effect may inhibit fast-growing viruses, thereby helping to facilitate coexistence.

Excess Risk of COVID-19 to University Populations Resulting from In-Person Sporting Events.

BACKGROUND: One of the consequences of COVID-19 has been the cancelation of collegiate sporting events. We explore the impact of sports on COVID-19 transmission on a college campus. METHODS: Using a compartmental model representing the university, we model the impact of influxes of 10,000 visitors attending events and ancillary activities (dining out, visiting family, shopping, etc.) on 20,000 students. We vary the extent visitors interact with the campus, the number of infectious visitors, and the extent to which the campus has controlled COVID-19 absent events. We also conduct a global sensitivity analysis. RESULTS: Events caused an increase in the number of cases ranging from a 25% increase when the campus already had an uncontrolled COVID-19 outbreak and visitors had a low prevalence of COVID-19 and mixed lightly with the campus community to an 822% increase where the campus had controlled their COVID-19 outbreak and visitors had both a high prevalence of COVID-19 and mixed heavily with the campus community. The model was insensitive to parameter uncertainty, save for the duration a symptomatic individual was infectious. CONCLUSION: Sporting events represent a threat to the health of the campus community. This is the case even in circumstances where COVID-19 seems controlled both on-campus and among the general population.

Predicting COVID-19 using past pandemics as a guide: how reliable were mathematical models then, and how reliable will they be now?

During the earliest stages of a pandemic, mathematical models are a tool that can be imple-mented quickly. However, such models are based on meagre data and limited biological understanding. We evaluate the accuracy of various models from recent pandemics (SARS, MERS and the 2009 H1N1 outbreak) as a guide to whether we can trust the early model predictions for COVID-19. We show that early models can have good predictive power for a disease's first wave, but they are less predictive of the possibility of a second wave or its strength. The models with the highest accuracy tended to include stochasticity, and models developed for a particular geographic region are often applicable in other regions. It follows that mathematical models developed early in a pandemic can be useful for long-term predictions, at least during the first wave, and they should include stochastic variations, to represent unknown characteristics inherent in the earliest stages of all pandemics.

A Quasi-Steady-State Approximation to the Basic Target-Cell-Limited Viral Dynamics Model with a Non-Cytopathic Effect.

Analysis of previously published target-cell limited viral dynamic models for pathogens such as HIV, hepatitis, and influenza generally rely on standard techniques from dynamical systems theory or numerical simulation. We use a quasi-steady-state approximation to derive an analytic solution for the model with a non-cytopathic effect, that is, when the death rates of uninfected and infected cells are equal. The analytic solution provides time evolution values of all three compartments of uninfected cells, infected cells, and virus. Results are compared with numerical simulation using clinical data for equine infectious anemia virus, a retrovirus closely related to HIV, and the utility of the analytic solution is discussed.

Dynamics of lentiviral infection in vivo in the absence of adaptive immune responses.

Understanding the dynamics of acute viral infection is crucial for developing strategies to prevent and control infection. In this study, lentiviral dynamics in a host without adaptive immunity were examined in order to determine kinetic parameters of infection and quantify the effect of neutralizing antibodies in preventing infection, using mathematical modeling of data from equine infectious anemia virus (EIAV) infection of horses with severe combined immunodeficiency (SCID). Estimated parameters were used to calculate the basic reproductive number and virus doubling time and found that the rate that antibodies neutralized virus was ~18 times greater than the virus clearance rate. These results establish EIAV replication kinetics in SCID horses and the minimal efficacy of antibodies that blocked infection. Furthermore, they indicate that EIAV is at most mildly cytopathic. This study advances our understanding of EIAV infection and may have important implications for the control of other viral infections, including HIV.

Antibody escape kinetics of equine infectious anemia virus infection of horses.

Lentivirus escape from neutralizing antibodies (NAbs) is not well understood. In this work, we quantified antibody escape of a lentivirus, using antibody escape data from horses infected with equine infectious anemia virus. We calculated antibody blocking rates of wild-type virus, fitness costs of mutant virus, and growth rates of both viruses. These quantitative kinetic estimates of antibody escape are important for understanding lentiviral control by antibody neutralization and in developing NAb-eliciting vaccine strategies.

Free-virus and cell-to-cell transmission in models of equine infectious anemia virus infection.

Equine infectious anemia virus (EIAV) is a lentivirus in the retrovirus family that infects horses and ponies. Two strains, referred to as the sensitive strain and the resistant strain, have been isolated from an experimentally-infected pony. The sensitive strain is vulnerable to neutralization by antibodies whereas the resistant strain is neutralization-insensitive. The sensitive strain mutates to the resistant strain. EIAV may infect healthy target cells via free virus or alternatively, directly from an infected target cell through cell-to-cell transfer. The proportion of transmission from free-virus or from cell-to-cell transmission is unknown. A system of ordinary differential equations (ODEs) is formulated for the virus-cell dynamics of EIAV. In addition, a Markov chain model and a branching process approximation near the infection-free equilibrium (IFE) are formulated. The basic reproduction number R0 is defined as the maximum of two reproduction numbers, R0s and R0r, one for the sensitive strain and one for the resistant strain. The IFE is shown to be globally asymptotically stable for the ODE model in a special case when the basic reproduction number is less than one. In addition, two endemic equilibria exist, a coexistence equilibrium and a resistant strain equilibrium. It is shown that if R0>1, the infection persists with at least one of the two strains. However, for small infectious doses, the sensitive strain and the resistant strain may not persist in the Markov chain model. Parameter values applicable to EIAV are used to illustrate the dynamics of the ODE and the Markov chain models. The examples highlight the importance of the proportion of cell-to-cell versus free-virus transmission that either leads to infection clearance or to infection persistence with either coexistence of both strains or to dominance by the resistant strain.

Estimating epidemic parameters: Application to H1N1 pandemic data.

This paper discusses estimation of the parameters in an SIR epidemic model from the observed longitudinal new infection count data. The potential problems of the standard MLE approaches are revealed and possible remedies suggested. The analysis is based on the epidemic data from the 2009 outbreak of H1N1 influenza on the campus of Washington State University.

Understanding virus-host dynamics following EIAV infection in SCID horses.

We develop a mathematical model for the interaction between two competing equine infectious anemia virus strains and neutralizing antibodies. We predict that elimination of one or both virus strains depends on the initial antibody levels, the strength of antibody mediated neutralization, and the persistence of antibody over time. We further show that the ability of a subdominant, neutralization resistant virus to dominate the infection transiently or permanently is dependent on the antibody-mediated neutralization effect. Finally, we determine conditions for persistence of both virus strains. We fit our models to virus titers from horses (foals) with severe combined immunodeficiency to estimate virus-host parameters and to validate analytical results.

Identifying the Conditions Under Which Antibodies Protect Against Infection by Equine Infectious Anemia Virus.

The ability to predict the conditions under which antibodies protect against viral infection would transform our approach to vaccine development. A more complete understanding is needed of antibody protection against lentivirus infection, as well as the role of mutation in resistance to an antibody vaccine. Recently, an example of antibody-mediated vaccine protection has been shown via passive transfer of neutralizing antibodies before equine infectious anemia virus (EIAV) infection of horses with severe combined immunodeficiency (SCID). Viral dynamic modeling of antibody protection from EIAV infection in SCID horses may lead to insights into the mechanisms of control of infection by antibody vaccination. In this work, such a model is constructed in conjunction with data from EIAV infection of SCID horses to gain insights into multiple strain competition in the presence of antibody control. Conditions are determined under which wild-type infection is eradicated with the antibody vaccine. In addition, a three-strain competition model is considered in which a second mutant strain may coexist with the first mutant strain. The conditions that permit viral escape by the mutant strains are determined, as are the effects of variation in the model parameters. This work extends the current understanding of competition and antibody control in lentiviral infection, which may provide insights into the development of vaccines that stimulate the immune system to control infection effectively.

Transmission-dynamic model to capture the indirect effects of infant vaccination with Prevnar (7-valent pneumococcal conjugate vaccine (PCV7)) in older populations.

We developed an age-structured, transmission-dynamic, mathematical model to quantify the direct and indirect benefits of infant PCV7 vaccination. The model simulates the acquisition of asymptomatic carriage of Streptococcus pneumoniae and the development of fatal and non-fatal invasive pneumococcal disease (IPD) among vaccinated and unvaccinated individuals aged <2, 2-4, 5-17, 18-49, 50-64, and >or=65 years old. The model was parameterized using published US surveillance data, supplemented with data from published literature. The model predicts the observed incidence of IPD with good agreement and may be used to predict the impact of various vaccination strategies in the US or other populations yet to introduce PCV7.

Differential immunogenicity of vaccinia and HIV-1 components of a human recombinant vaccine in mucosal and blood compartments.

Mucosal immune responses induced by HIV-1 vaccines are likely critical for prevention. We report a Phase 1 safety and immunogenicity trial in eight participants using the vaccinia-based TBC-3B vaccine given subcutaneously to determine the relationship between HIV-1 specific systemic and gastrointestinal mucosal responses. Across all subjects, detectable levels of blood vaccinia- and HIV-1-specific antibodies were elicited but none were seen mucosally. While the vaccinia component was immunogenic for CD8(+) T lymphocyte (CTL) responses in both blood and mucosa, it was greater in blood. The HIV-1 component of the vaccine was poorly immunogenic in both blood and mucosa. Although only eight volunteers were studied intensively, the discordance between mucosal and blood responses may highlight mechanisms contributing to recent vaccine failures.

Predicting the potential impact of a cytotoxic T-lymphocyte HIV vaccine: how often should you vaccinate and how strong should the vaccine be?

To stimulate the immune system's natural defenses, a post-infection HIV vaccination program to regularly boost cytotoxic T-lymphocytes has been proposed. We develop a mathematical model to describe such a vaccination program, where the strength of the vaccine and the vaccination intervals are constant. We apply the theory of impulsive differential equations to show that the model has an orbitally asymptotically stable periodic orbit, with the property of asymptotic phase. We show that, on this orbit, the vaccination frequency can be chosen so that the average number of infected CD4(+) T cells can be made arbitrarily low. We illustrate the results with numerical simulations and show that the model is robust with respect to both the parameter choices and the formulation of the model as a system of impulsive differential equations.

Effectiveness and efficiency of imperfect therapeutic HSV-2 vaccines.

BACKGROUND: Efforts are currently underway to develop therapeutic vaccines for Herpes Simplex Virus type 2 (HSV-2). METHODS: We use a mathematical model to predict the potential public health impact of imperfect, therapeutic HSV-2 vaccines. We evaluate vaccine effectiveness and efficiency for the general population in the United States where HSV-2 prevalence is currently 22%. We assume that therapeutic vaccines will produce two therapeutic benefits in vaccinated infected-individuals: (i) the rate of viral reactivation will decrease (hence infected-individuals will experience fewer viral shedding episodes), and (ii) the average length of the viral shedding episodes will be shortened. In addition, we assume that therapeutic vaccines will benefit uninfected individuals by reducing viral shedding in (and hence transmission from) vaccinated infected-individuals. RESULTS: Our predictions show that therapeutic vaccines could substantially reduce HSV-2 epidemics by reducing new infections by 77% and preventing 0.84 new infections for each vaccinated individual. These vaccines could prevent 212,600 (median; IQR, 156,064-288,558) new infections after only one year. We show that increased effectiveness and efficiency are more strongly correlated with a vaccine-induced reduction in transmission probability than with either of the two therapeutic benefits that accrue directly to the infected individuals (specifically, the reduction in episode length and number of episodes). CONCLUSIONS: We suggest that current vaccine development efforts target mechanisms that reduce viral shedding (thereby reducing transmission) thus providing both a beneficial therapeutic and a beneficial epidemic-level impact. Our results also demonstrate that therapeutic vaccines would be substantially more useful than prophylactic vaccines for epidemic control.

Modeling the potential impact of rectal microbicides to reduce hiv transmission in bathhouses.

We evaluate the potential impact of rectal microbicides for reducing HIV transmission in bathhouses. A new mathematical model describing HIV transmission dynamics among men who have sex with men (MSM) in bathhouses is constructed and analyzed. The model incorporates key features affecting transmission, including sexual role behavior (insertive and receptive anal intercourse acts), biological transmissibility of HIV, frequency and efficacy of condom usage, and, most pertinently, frequency and efficacy of rectal microbicide usage. To evaluate the potential impact of rectal microbicide usage, we quantify the effect of rectal microbicides (ranging in efficacy from 10% to 90%) on reducing the number of HIV infections in the bathhouse. We conduct uncertainty analyses to assess the effect of variability in both biological and behavioral parameters. We find that even moderately effective rectal microbicides (if used in 10% to 50% of the sex acts) would substantially reduce transmission in bathhouses. For example, a 50% effective rectal microbicide (used in 50% of sex acts) would reduce the number of secondary infections by almost 13% at disease invasion. Our modeling analyses show that even moderately effective rectal microbicides could be very effective prevention tools for reducing transmission in bathhouses and also potentially limit the spread of HIV in the community.

Highly active antiretroviral therapy and the epidemic of HIV+ end-stage renal disease.

The rise in the number of patients with HIV-associated nephropathy and HIV-infection with end-stage renal disease (HIV+ ESRD) continues to be a substantial concern for the ESRD program. In order to assess the impact of highly active antiretroviral therapy (HAART) on the progression of patients with AIDS to the development of ESRD and to project the prevalence of HIV+ ESRD through 2020, a mathematical model of the dynamics of HIV+ infection in the ESRD population was developed. Epidemiologic data on AIDS and HIV+ ESRD among black individuals in the United States were obtained since 1991 from the Centers for Disease Control and Prevention and US Renal Data System, respectively. The model was constructed to predict the prevalence of HIV+ ESRD incorporating the current rate of growth in AIDS prevalence. Two possible trends were considered: linear AIDS growth and exponential AIDS growth. The likely effectiveness of HAART in slowing progression to HIV+ ESRD was estimated from the best fit of the model to the data after 1995, when HAART was introduced. The model was then used to evaluate recent data and to project the prevalence of HIV+ ESRD through 2020. The model suggested that HAART has reduced the rate of progression from AIDS to HIV+ ESRD by 38%. The model projected an increase in HIV+ ESRD prevalence in the future as a result of the increase in the AIDS population among black individuals. This increase was predicted even assuming a 95% reduction in the progression from AIDS to HIV+ ESRD. Despite the potential benefit of HAART, the prevalence of HIV+ ESRD in the United States is expected to rise in the future as a result of the expansion of the AIDS population among black individuals. It is concluded that prevention of progression to ESRD should focus on early antiretroviral treatment of HIV-infected patients who have evidence of HIV-associated nephropathy.

Predicting the potential individual- and population-level effects of imperfect herpes simplex virus type 2 vaccines.

BACKGROUND: The seroprevalence of herpes simplex virus (HSV) type 2 in the United States has increased dramatically since the 1970s. Vaccines are being developed to control the epidemic. We determined the potential public health impact that imperfect, preexposure HSV-2 vaccines could have on reducing the incidence of infection. METHODS: We modeled the future impact of preexposure vaccines with both prophylactic and therapeutic properties. We predicted the individual-level (cumulative number of new infections prevented per 1000 vaccinated individuals) and population-level (cumulative percentage reduction in new infections) impact. RESULTS: We show that the percentage reduction in incidence of infection would be relatively modest. However, HSV-2 incidence rates are extremely high; thus, we calculate that even imperfect vaccines would prevent >1 million infections in the United States within a decade after introduction. We found that vaccines would prevent 3 times as many infections per vaccinated person in a high-prevalence epidemic than in a moderate-prevalence epidemic. We also identified the vaccine characteristics that have the greatest impact on reducing the incidence of infection. We determined that vaccine take and degree of protection against infection are equally important, whereas therapeutic characteristics are unimportant. CONCLUSIONS: Designing preexposure HSV-2 vaccines with therapeutic characteristics will have little impact on reducing the incidence of infection. HSV-2 vaccines will have a substantially greater public health impact in developing than in developed countries.