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¶ Members of the WHO-VMI Dengue Vaccine Modeling Group are listed in the Acknowledgments.

Dengue viruses are single-stranded positive-sense RNA viruses (genus

The most advanced dengue vaccine candidate—a live-attenuated, tetravalent, chimeric yellow fever dengue vaccine—commenced Phase II and Phase IIB clinical trials in 2009, and Phase III trials in December of 2010

In line with the theory behind ADE, subneutralizing antibody concentrations—theoretically occurring when immunity is waning or between vaccine doses—represent a potential risk of severe dengue to patients infected with wild-type virus during this critical period. This individual-level risk can be evaluated with sufficient follow-up, but population-level effects cannot be analyzed in the context of a vaccine trial. Population-level immunity may change the proportion of infections that occur in individuals with partial immunity, and these infections may be associated with higher viraemia and thus possibly higher transmission, generating a potential indirect detrimental effect of vaccination

Population-level effects, whether related to ADE or not, can be analyzed with mathematical models. Since it is not feasible to enroll and randomize populations to dengue vaccine or placebo, mathematical models may provide the only environment where multiple types of population-wide dengue strategies can be evaluated. Models allow for assessment of multiple intervention and evaluation strategies. They can be used to understand the specific population-level mechanisms by which vaccines reduce incidence and can aid in the design of evaluation studies. The World Health Organization (WHO) has recommended that mathematical models be used to assess and inform various methods of new vaccine introductions

To date, most models of dengue transmission have been limited in scope and focused on specific questions in transmission dynamics. However, many aspects of the dynamics of dengue transmission are still not fully understood. In order for models to be accurate, realistic, and useful, there is an urgent need for improved understanding of dengue virology and immunology, as well as the entomological, social, and environmental factors that modulate dengue transmission. As these facets of dengue biology are further investigated, we will gain confidence that future mathematical models may come close to an accurate representation of true dengue epidemics.

A mathematical model is a set of equations or rules describing how a certain process unfolds in time. Manipulating these rules allows one to experiment with components of the model to explore their effects on the modeled process as a whole, and it allows one to compare predicted model outcomes with observed data. Mathematical models of disease transmission have three main purposes: understanding the fundamental driving forces of disease ecology and epidemiology, measuring epidemiological parameters that cannot be directly measured with field or laboratory data, and making predictions of future disease incidence under specified conditions. Recent applied dengue modeling examples include models to explore and validate the effects of weather on the mosquito life cycle

The disease state space of five alternative dengue model structures incorporating immune enhancement and short-term cross protection are shown. The disease states are: _{i} infectious with serotype _{ij} infectious with serotype _{i} recovered from and immune to serotype _{ij} recovered from and immune to serotypes _{ij} indicated by red arrows showing an increase in the rates of acquisition of primary and secondary infection due to this effect. Model (_{ij} to a mosquito species. Note that in this formulation, mosquitoes that have obtained infection from a secondary human infection are not more likely to transmit to humans. Subscripts

Dengue modeling has been useful in helping us understand the virus' dynamics and in generating some new hypotheses about why the dynamics exhibit certain irregularities, both short-term and long-term. Nevertheless, when compared to diseases such as influenza or malaria, the dengue modeling literature is sparse and focused on a small number of topics, often serotype oscillations or antibody-dependent enhancement. Given the importance of mosquito populations to dengue transmission, we have a relatively poor understanding of their population dynamics. In addition, dengue models are rarely analyzed with a public health goal in mind, and very little modeling has been done to evaluate dengue interventions.

In developing an appropriate mathematical model (or set of models) for dengue vaccination, the main challenge lies in resolving the complexity of interactions among host immune status, demography, vector populations, and environmental factors. A current focus of much modeling work is the strong interaction between dengue immunology and epidemiology. Through conferral of immunity, dengue epidemics generate population-wide immune profiles that subsequently determine the severity, speed, and magnitude of dengue's second pass through that same population. Typically, as a dengue epidemic progresses, surveillance focuses on case numbers and severity without recording changes in immune status; this deprives us of essential data necessary for understanding the immuno-epidemiology of dengue. One of the greatest challenges for epidemiologists and mathematical modelers alike may be determining study designs that can collect data on host immune status as efficiently and completely as possible; such data sets may allow us to describe the dynamics of population-wide immunity and its effects on future disease incidence.

Because we do not yet have a well-tested general model of dengue immuno-epidemiology, we cannot predict accurately how a TDV would alter future dengue dynamics. Mathematical modeling research must thus start by identifying realistic expectations for a TDV campaign, given a varied set of scenarios for vaccine introduction in a population. These analyses may need to evaluate if TDV rollout will have a greater impact on case numbers or severity, and if vaccination-induced shifts in the age burden have positive or negative impacts on overall disease severity.

The next challenge will be to create a set of public health objectives that will define the success of a dengue vaccination campaign. Reduced case numbers, fewer severe cases, and fewer deaths are all potential marks of success, but these three indicators may not correlate with one another, either in the population as a whole or across age classes. For example, dengue in the elderly can be complicated by comorbidities that increase the risk of severe outcomes

Because the interactions among key determinants of dengue transmission, such as environmental factors and vector biology, are not well understood, exploring the role of these determinants through modeling will require significant effort. There are still gaps in our understanding of short-term cross protective immunity

To address these uncertainties and to accelerate the development of mathematical models that can evaluate dengue vaccination strategies, WHO and the Vaccine Modeling Initiative (VMI) convened a group of dengue epidemiologists, clinicians, immunologists, public health officials, vaccine developers, entomologists, and mathematical modelers to discuss possibilities for assessing the population-wide impact of a tetravalent dengue vaccine. This was the first such meeting, which was hosted by WHO in late 2010. Its purpose was to establish (1) a forum for an inter-disciplinary working group to discuss the development of optimal dengue vaccination strategies, and (2) future meetings with more experts and stakeholders in dengue vaccination. The WHO-VMI Dengue Vaccine Modeling Group's first phase of collaboration has begun by linking modelers with epidemiologists, clinicians, immunologists, and vaccine developers for the purpose of conducting preliminary modeling analyses on the risks and benefits of dengue vaccination.

The initial questions identified by the group as critical in assessing a dengue vaccine are listed in

Are there vaccine product profiles that could lead to increased transmission from secondary infections?

What changes in age distribution of primary and secondary infection are expected after vaccine introduction and mass immunization?

Given the demographics and force of infection in any particular setting, what is the optimal age of vaccination and/or the age-stratified critical vaccination fraction?

If vaccine efficacy depends on pre-existing immunity, what is the optimal age of vaccination and/or the age-stratified critical vaccination fraction?

Should a vaccination strategy change given geographical variation in transmission?

How should catch-up campaigns be implemented?

What immune escape or other viral evolutionary responses can be expected?

How should the immune system be represented in models?

How should individual risk profiles (i.e., the characteristics of an individual, including past infections and vaccination status, that affect the individual's risk for severe dengue) be defined and modeled?

How should population-level vaccine effects be monitored?

The utility of models to assess vaccine candidates depends on the models' ability to represent transmission dynamics accurately. Measuring or estimating model parameters is therefore a critical step in constructing an accurate dengue model. Some parameters can be measured directly from epidemiological or laboratory data (duration of viraemia, mean age of first infection), while in other cases models may be used to statistically infer the impacts of certain features of transmission dynamics that cannot be measured directly (duration of cross-protective immunity

Many of the individual-level parameters concerning immunity and disease severity are ideally measured in prospective cohort studies with long-term follow up.

Location | Years | Ages | Follow-Up | Population with Follow-Up | Notes | Reference |

Bangkok, Thailand | 1962–1964 | All ages | 6–11 months | 1,887 | Includes entomological indices and hospitalization data. | |

Koh Samui, Thailand | 1966–1967 | 2–12 years | 1 year | 336 | ||

Yangon, Myanmar | 1984–1988 | 2–6 years | 1 year | 3,579 | Five separate cohorts started each year. Includes hospitalization data. | |

Bangkok, Thailand | 1980–1981 | 4–16 years | 6 months | 1,757 | ||

Rayong, Thailand | 1980–1981 | 4–14 years | 1 year | 1,056 | ||

Iquitos, Peru | 1993–1996 | 7–20 years | 2.5 years | 129 | No DHF/DSS found in secondary cases. | |

Bangkok+Khamphaeng Phet, Thailand | 1994–1996 | 6 months –14 years | 1 year | 168 | 48 had follow-up past 180 days. | |

Yogyakarta, Indonesia | 1995–1996 | 4–9 years | 1 year | 1,837 | ||

Khamphaeng Phet, Thailand | 1998–ongoing | 7–11 years | 2 years | 2,119 | Study performed in two periods: 1998–2002, 2004–2006 | |

Bandung, West Java, Indonesia | 2000–2002 | 18–66 years | 2 years | 2,536 | ||

West Jakarta, Indonesia | 2001–2003 | Children and adults | 14 days; 6 months for cases | 785 | Cluster investigation enrolling contacts of known cases. | |

Managua, Nicaragua | 2001–2003 | 4–16 years | 1–2 years | 999 | ||

An Giang, Vietnam | 2004–2007 | 2–15 years | 3 years | >3,000 | Additional children recruited every year. 1,594 children had 3 years of follow-up. | |

Managua, Nicaragua | 2004–ongoing | 2–9 years | 4 years | 3,721 | Includes entomological indices. | |

Ho Chi Minh City, Vietnam | 2006–2007 | Newborns enrolled | 1 year | 1,244 infants | ||

Ratchaburi, Thailand | 2006–2010 | 3–15 years | 4 years | ∼3,000 | Study ended. | Unpublished |

Colombo, Sri Lanka | 2008–2010 | <12 years | 2 years | 800 | Study ended. | Unpublished |

Ho Chi Minh City, Vietnam | 2009–ongoing | Newborns | 1 year | ∼3,000 infants | Unpublished |

For all those involved—whether in epidemiology, in clinical or laboratory settings, or as modelers—it is critical that complete data sets and the analysis of that data be shared so that all the partners can come to a common understanding of the interpretation of the data. The recent meeting in 2010 sought to catalyze this effort by taking advantage of the participants' varied skills and experiences and by bringing together those scientists specializing in theory/modeling with those that have a detailed understanding of the data. Sharing and analyzing data from ongoing and past studies will be critical for building robust mathematical models of dengue. The first small step in this partnership will be the joint design and analysis of mathematical models rooted in the most recent epidemiological and laboratory data, with each collaboration including modelers and non-modelers.

In addition to sharing data sets and analyses and interpreting results, we must recognize that dengue vaccination planning will probably happen alongside vector control, social outreach and educational campaigns, multiple types of surveillance, expansion of local capacity to diagnose and manage dengue, and perhaps novel entomological approaches of reducing transmission by altering mosquito ecology or genetics

The mathematical models developed through the joint effort of the modeling community and dengue community will give us prediction and evaluation tools that can be used to determine optimal vaccination strategies for each endemic country. Recommendations will be discussed with national public health authorities and adapted to the requirements and realities of the host countries. When an implementation method is chosen for rolling out dengue vaccines, appropriate and timely surveillance activities should be planned so that the effectiveness of the vaccination strategy can be tested and adjusted in real time. The implemented strategy will almost certainly not be the one determined to be optimal by a mathematical model, but one that combines relevant aspects of feasibility, cost-effectiveness, political acceptability, and public health benefits. We must recognize that mathematical models are at best fallible as prediction tools and that the implementation process itself will reveal new trends and facts that can be used to improve future models and recommendations.

The WHO-VMI Dengue Vaccine Modeling Group consists of a group of experts in dengue epidemiology, clinical practice, immunology, virology, vaccinology, entomology, and mathematical modeling. All contributed to the writing of this Policy Forum. In alphabetical order, the group members and contributing authors are

Laurent Coudeville, Jean Lang, and Remy Teyssou are employees of Sanofi-Pasteur (France). Adrienne Guignard, Gerhart Knerer, and Baudoin Standaert are employees of GSK Biologicals (Belgium). Joachim Hombach and Pem Namgyal are staff members of the World Health Organization. This report contains the collective views of an international group of experts, and does not necessarily represent the decisions or the stated policy of the World Health Organization. All other authors have declared that no competing interests exist.

This work was primarily funded by the World Health Organization, and funded in part by the Gates Foundation's Vaccine Modeling Initiative, the Dengue Vaccine to Vaccination Initiative (v2V), and the Pediatric Dengue Vaccine Initiative (PDVI). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.