This workshop is an offshoot of the DIMACS Working Group on Methodologies for Comparing Vaccination Strategies.
Title: Influenza antigenic drift in vaccinated populations
I will present a mathematical model to study the evolution of influenza A during the epidemic dynamics of a single season. Classifying strains by their distance to the epidemic-originating strain, it can be shown that neutral evolution yields a constant rate of antigenic drift, even in the presence of epidemic dynamics. Introducing host immunity, as will be the case in vaccinated human populations, I will present a non-neutral model whose population dynamics can be framed naturally in the context of population genetics. It can be show that departure from neutrality is governed by the covariance between a strain's fitness (immunity escaped) and its distance to the original epidemic strain. This departure from neutrality can then be quantified as a function of the model parameters.
Title: Predicting Human Papilloma Virus Prevalence and Vaccine Policy Effectiveness in Demographic Strata
Human Papilloma Virus (HPV) is a sexually transmitted virus, which can lead to cervical cancer. HPV DNA is found in cervical cancers with types 16, 18, 31 and 45 accounting for more than 75 % of cervical cancers. Candidate vaccines have entered phase III testing with the Food and Drug administration and several drug companies are in licensing arbitration. Once this vaccine becomes available, an effective vaccination strategy is needed. Hughes, Garnett and Anderson have developed a model to predict HPV prevalence and population-level vaccine effectiveness; however, this model does not allow for stratification with time-dependent demographic traits, such as age. With this in mind, we have developed a tool that facilitates predicting HPV prevelence in a variety of demographic settings and allows for quantification of different vaccination policies.
Title: A multi-type human papillomavirus vaccination model with antagonism and synergism
Vaccines against the most common human papillomavirus (HPV) types are currently under development. Epidemiologic data suggest that the transmission dynamics of the current HPV types are not independent. Some studies indicate that interactions among HPV types are synergistic, where infection with one type facilitates concurrent or subsequent infection with another HPV type. Other studies point to antagonistic interference among HPV types. Here we develop a mathematical model to explore how these interactions may either enhance or diminish the effectiveness of vaccination programs designed to reduce the prevalence of the HPV types associated with cervical cancer. We analyze the local stability of the infection-free and boundary equilibria and characterize the conditions leading to a coexistence equilibrium. We also illustrate the results with numerical simulations using realistic model parameters. We show that if interactions among HPV types are synergistic, mass vaccination may reduce the prevalence of types that are not even included in the vaccine.
Title: Vaccinating against influenza
Influenza A viruses impose a heavy morbidity and mortality burden on the human population, both through annual epidemics and through occasional 'pandemics' that involve the spread of new antigenic 'subtypes'. I will discuss influenza evolution and population biology, and introduce some issues in influenza vaccination policy.
Title: The evolution of HIV-1 virulence
HIV-1 recently entered humans from its natural chimpanzee host, which has led to speculation that the virus may have adapted or may continue to adapt to spread within the human population. Analysis of data on the associations between viral load, infectiousness and survival suggest that HIV-1 follows the now "classical" evolutionary trade-off paradigm, where gains in infectiousness come at the cost of losses in life-expectancy and opportunities for transmission are maximised for intermediate virulence levels. HIV-1 is found to be near optimal with respect to this trade-off, effectively maximising the lifetime number of people a person can infect (at least for populations where spread is predominantly heterosexual). A simulation is developed and shows that this adaptation could have arisen prior to the 1980s (when the virus was discovered). This suggests that without intervention, there will be little or no future change in virulence for HIV-1. I will speculate as to the effects that mass treatment or vaccination could cause in changing this balance.
Title: Imperfect vaccines, within-host dynamics and parasite evolution
Vaccines rarely provide full protection from disease. Nevertheless, partially effective (imperfect) vaccines may be used to protect both individuals and whole populations. We studied the potential impact of different types of imperfect vaccines on the evolution of pathogen virulence (induced host mortality) and the consequences for public health. We previously showed that vaccines designed to reduce pathogen growth rate and/or toxicity may promote the evolution towards higher levels of intrinsic virulence and hence more severe disease in unvaccinated individuals [1-3]. Here we will present a more sophisticated version of this model that combines a microscopic (within-host dynamics) and a macroscopic (epidemiological dynamics) description of the interaction between the parasite and its host [4]. This approach allows relevant epidemiological traits like parasite transmission, parasite virulence and host recovery to emerge from a mechanistic model of acute infection describing the interaction between the parasite and the host immune system. We model the effect of a vaccine as an activator of immunity enhancing the replication rate of lymphocytes, their initial density at infection's initiation, their efficacy to kill the parasite or their activation delay after infection. We analyze the evolution of the replication rate of parasites and show that vaccination may promote the evolution of faster replicating and,consequently, more virulent strains. We also show that intermediate vaccination coverage may lead to the coexistence of two different parasite strategies (a low virulence strain adapted to naïve hosts, and a high virulence strain, more generalist, adapted to both naïve and vaccinated hosts). We discuss the consequences of various vaccination strategies under different epidemiological situations using several distinct measures to evaluate the cost induced by the parasite on individuals and whole host populations.
Title: The reinfection threshold and its consequences for vaccination
The reinfection threshold has been recently introduced in infectious disease epidemiology, and is finding an increasing number of applications. First, populations that exceed this threshold sustain high levels of infection and tend to be insensitive to vaccination, leading to a simple mechanism for the controversial variable efficacy of the bacille Calmette-Gurin (BCG) vaccine against pulmonary tuberculosis. Second, a reinfection threshold appears to have a regulatory role in pathogen diversity, leading to a proposed mechanism for the unusual patterns of influenza evolution. In pertussis and malaria, this seems to underlie the positioning of maximal disease burden at intermediate levels of transmission. Reinfection thresholds appear responsible for a number of unresolved inconsistencies reported in recurrent infections, but perhaps the most exciting is that they can be manipulated by suitable vaccines and used in control planning. This practical implication has never been explored.
Title: Phylodynamics of acute microparasites and the impact of vaccination
We use models and analyses of empirical data to explore the interaction of pathogen epidemiological and evolution ary dynamics and implications for vaccination. We focus especially on the dynamics of equine influenza.
Title: Role of evolution of virulence in study designs and measurement of vaccine efficacy
In this talk, we consider issues of study design and analysis related to vaccine studies when the vaccine puts evolutionary pressure on the infectious agent. This includes considerations when there are multiple concurrent strains present, or when a new evolutionary strain might replace another.
Title: Virulence evolution in malaria parasites - data and theory
Virulence evolution of microparasites (e.g. Plasmodium) is thought to be driven by the parasite's need to transmit to new hosts (parasite fitness), with virulence being an unavoidable side-effect of this driving evolutionary force. This theory, though widely propounded, is poorly supported by data for any pathogen. We therefore set out to test this hypothesis in malaria - a widespread killer of humans - using the rodent malaria, P. chabaudi, as a laboratory model. We found overwhelming evidence in support of it1,2. Using data from field studies, we showed that the hypothesis is also strongly supported for human malaria with parasite fitness being maximised in the most vulnerable class of hosts3. Immunity to malaria is always only partial. We showed that host immunity acts to decrease virulence and, through its intrinsic link with transmission described above, parasite fitness4. Therefore it is expected that immunity will select parasites for higher virulence. We used this principle in an evolutionary-epidemiological model to predict that widespread use of imperfect vaccines would lead to the evolution of more virulent parasites5. This hypothesis, which relies on between-host selection processes via the mosquito is unable to be tested in the laboratory. However, by performing experimental evolution of parasites in mice, we found that within-host selection processes led parasites to evolve higher virulence more rapidly in immune hosts than in non-immune hosts6. We have also showed that mosquito transmission plays a role in these evolutionary processes.
Title: Mathematical models of the evolution and spread of infections
There is an increasing body of evidence that describes the acquisition and loss of immune escape mutants in HIV infected individuals. It is now clear that these escape mutants are widely present, have an impact upon infected individuals' viral loads and, by implication, play an important role in the epidemiology of HIV. Thus escape mutants are an important issue for individual pathogenesis, but also need to be considered as a factor in the ongoing pandemic. The population dynamics of these immune escape mutants is driven by at least three processes:
Because of the multiple processes driving their dynamics, understanding how the abundance of different variants will change through time is not a trivial task. However it is likely that they are already playing an important role in the existing pandemic and will need to be considered when an effective vaccine becomes available. Understanding the evolution of escape mutants at a population level is therefore critical. More generally, pathogens evolve within individuals and are constantly transmitted between individuals so experience ceaselessly shifting selective pressures. This talk will introduce new mathematical models that capture these processes. Existing models of pathogen diversity treat either within-host processes or between-host processes. These new models set out to describe events at both levels simultaneously.The talk will present some of the biological data that motivates these models, describe the construction of simple version of these models, give early results and discuss future directions in which this new family of mathematical models will need to be driven.
The talk will present some of the biological data that motivates these models, describe the construction of simple version of these models, give early results and discuss future directions in which this new family of mathematical models will need to be driven.
Title: The genetic drift of influenza A
Influenza A is an infectious disease with evolutionary dynamics resulting in a characteristic phylogenetic tree, having a 'single trunk' shape. We developed and studied a model with strain-independent short-term immunity and strain-dependent long-term immunity (cf. Ferguson et al. 2003) providing reduced transmission by cross-immunity (analogous to Gog and Grenfell, 2002), where cross-immunity between two arbitrary strains is the product of the cross-immunity of all their parents. Furthermore, we assume higher transmission during winter, stochastic survival during summer, and homogeneous mixing in two alternating, loosely connected subpopulations (cf. temperate climate zones). The model shows yearly epidemics and competitive exclusion of viral strains, resulting in a single trunk-like phylogenetic tree. We will discuss the validity of the model relating to important issues in influenza strain selection, evolution, vaccination, and pandemic planning.
This is a joint work with Sander van Noort, Jacco Wallinga and Odo Diekman.
Title: The impact of vaccination on the evolution of Marek's disease and malaria
This talk is in two halves, linked only by alliteration. Marek's disease is a viral poultry disease which became more virulent over the second half of the 20th Century. I will review evidence that this evolutionary change was caused by vaccination. It might have been, though there are other possibilities. Malarial infections frequently consist of several different parasite genotypes. It is well known from theoretical models that within-host genetic diversity can select for increased virulence. I will summarize our experimental work which supports this view, and ask whether vaccination will intensify or weaken that selection pressure.
Title: Game theory of vaccination against infectious diseases
Recent vaccine shortages and vaccine scares remind us that the effectiveness of mass vaccination programs is influenced by the public perception of vaccination. Previous work has shown that the tendency of individuals to optimize self-interest can lead to suboptimal implementations of vaccination policies for a community. In this talk, I'll discuss how game theory can be used to incorporate changing behavior into dynamic epidemiological models, and how behavior influences optimal policy determination.
Title: Predicting the Potential Individual-level and Population-level Effects of Imperfect HSV-2 Vaccines
Background: The seroprevalence of Herpes Simplex Virus type 2 (HSV-2) in the US has increased dramatically since the 1970s. Vaccines are being developed to control the epidemic. We determined the potential public health impact that imperfect, pre-exposure and post-exposure HSV-2 vaccines could have on reducing incidence.
Methods: We modeled the future impact of HSV-2 vaccines with both prophylactic and therapeutic properties. We predicted the individual-level (cumulative number of new infections prevented/1000 vaccinated individuals) and population-level (cumulative percentage reduction in new infections) impact.
Results: We show that the percentage reduction in incidence would be relatively modest with pre-exposure vaccines. However, HSV-2 incidence rates are extremely high; thus we calculate that even imperfect vaccines could prevent over 1 million infections in the US within a decade after introduction. We found that vaccines would prevent three 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 incidence. We determined that vaccine take and degree of protection against infection are equally important, whereas therapeutic characteristics are unimportant. With post-exposure vaccines, we found that the percentage reduction in incidence would be substantially greater than with pre-exposure vaccines.
Conclusions: Post-exposure vaccines would be more useful than pre-exposure vaccines for epidemic control. Designing pre-exposure HSV-2 vaccines with therapeutic characteristics will have little impact on reducing incidence. Such vaccines will have substantially greater public health impact in developing countries than in developed countries.
Title: Evolutionary considerations in HIV-1: Implications for HIV-1 vaccine development
Many believe that the global AIDS epidemic can only be controlled through the introduction of an effective vaccine. Yet, a generation after HIV-1 was first identified as the causative agent of AIDS, there is no vaccine available. This presentation will review the major strategies that have been employed in HIV vaccine development, and focus on current efforts to develop a vaccine capable of inducing an appropriate cell-mediated immune response. In addition, the talk will also address some general challenges in vaccine development along with discussion of specific characteristics of HIV-1 that pose challenges in vaccine development.
Title: The optimal amount of antiviral control
Antiviral agents have been hailed to hold considerable promise for the treatment and prevention of viral diseases such as influenza A and SARS. Here we explore, by means of epidemic models, the advantages and disadvantages of large-scale antiviral control. The analyses are based on the premise that, on the one hand, antiviral treatment may prevent infection and transmission but, on the other hand, is not completely harmless. Using life expectancy as the objective function we show how, in the endemic equilibrium, the interests of the public health officer relate to those of the individual. It appears that in many instances there is an incentive for individuals to invest less in antiviral therapy than would be optimal from the population perspective. Next, we extend the analyses by considering a myopic objective function that considers a time horizon much smaller than total life span (one week to a year). It appears that the optimal amount of antiviral control may be increased or decreased considerably if a finite instead of infinite time horizon is considered. Finally, we investigate the timing of the antiviral response during an epidemic, and conclude that it is far from clear how rational decisions should be taken in an ongoing epidemic. We discuss the implications of our results for the use of antiviral treatment as a control measure aimed at combatting viral pathogens.
This is a joint work with Don Klinkenberg, Ido Pen, Franz J. Weissing and Hans Heesterbeek.
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