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ABSTRACT: Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice--rather than accessibility--is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.
Journal of Theoretical Biology 12/2010; 267(3):276-82. · 2.21 Impact Factor
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ABSTRACT: Large-scale vaccination campaigns (SIAs) and improved routine immunization (RI) have greatly reduced measles incidence in low-income countries. However, the interval between SIAs required to maintain these gains over the long term is not clear. We developed a dynamic model of measles transmission to assess measles vaccination strategies in Cambodia, Ghana, India, Morocco, Nigeria, and Uganda. We projected measles cases from 2008 to 2050 under (a) holding SIAs every 2, 4, 6, or 8 years, (b) improvements in first dose routine measles vaccine (MCV1) coverage of 0%, 1%, 3% annually, and (c) introducing MCV2 once MCV1 coverage reaches 70%, 80%, 90%. If MCV1 continues improving, then India and Nigeria could hold SIAs every 4 years without significant probability of large outbreaks, and the other countries every 6-8 years. If RI remains stagnant, India and Nigeria should hold SIAs every 2 years, and the other countries every 4-6 years.
Vaccine 06/2009; 27(31):4090-8. · 3.77 Impact Factor
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ABSTRACT: Hepatitis A (HA) vaccination in Canada is currently targeted toward high-risk groups. The cost-effectiveness and expected health outcomes of universal vaccination relative to targeted vaccination in low-incidence countries such as Canada are currently unknown. Here, we conducted a cost-utility analysis for this situation, with Canada as the study population. We included vaccine costs, time costs, infection costs, and public health costs. We assessed a range of possible universal vaccination strategies over an 80-year time horizon using multiple cost perspectives. A dynamic model was used to account for herd immunity. Aggregate health gains from switching to universal vaccination are modest (10-30 QALYs per year). However, a "9+9" strategy that replaces two doses of monovalent hepatitis B (HB) vaccine at 9/10 years (universally administered in most provinces) with two doses of bivalent HA/HB vaccine is cost-saving from the societal perspective. At a willingness to pay threshold of $50,000/QALY, mean net benefit is +49.4 QALYs (S.D. 12.6) from the societal perspective and +3.8 QALYS (S.D. 3.0) from the payer perspective for the "9+9" strategy. Net benefit from the payer perspective is sensitive to the marginal cost of HA/HB vaccine relative to HB vaccine. Similar conclusions may apply in other countries with low incidence and a targeted vaccination policy.
Vaccine 01/2008; 25(51):8536-48. · 3.77 Impact Factor
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ABSTRACT: Vaccination against Hepatitis A virus (HAV) in Canada is currently targeted toward high-risk groups. However, universal vaccination has been adopted in several other countries with a similar disease burden. Here we develop an age-structured compartmental model of HAV transmission and vaccination in Canada to assess potential universal vaccination strategies. The model predicts that universal vaccination at age 1 (respectively 4, 9, 15), with phasing out of targeted vaccination, would reduce reported incidence by 60% (respectively 52, 36, 31%) and mortality attributable to HAV by 56% (respectively 45, 26, 25%), relative to continued targeted vaccination, over 80 years.
Vaccine 03/2007; 25(10):1719-26. · 3.77 Impact Factor
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ABSTRACT: Voluntary vaccination policies for childhood diseases present parents with a subtle challenge: if a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude complete eradication of a vaccine-preventable disease. We show that a formal game theoretical analysis of this problem leads to new insights that help to explain human decision-making with respect to vaccination. Increases in perceived vaccine risk will tend to induce larger declines in vaccine uptake for pathogens that cause more secondary infections (such as measles and pertussis). After a vaccine scare, even if perceived vaccine risk is greatly reduced, it will be relatively difficult to restore prescare vaccine coverage levels.
01/2004; 101:13391-13394.
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ABSTRACT: Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.
01/2003; 270:1573-1578.
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ABSTRACT: The recent threat of bioterrorism has fueled debate on smallpox vaccination policy for the United States. Certain policy proposals call for voluntary mass vaccination; however, if individuals decide whether to vaccinate according to self-interest, the level of herd immunity achieved may differ from what is best for the population as a whole. We present a synthesis of game theory and epidemic modeling that formalizes this conflict between self-interest and group interest and shows that voluntary vaccination is unlikely to reach the group-optimal level. This shortfall results in a substantial increase in expected mortality after an attack.
01/2003; 100:10564-10567.
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C T Bauch
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ABSTRACT: We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1). to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2). to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate.
Journal of Mathematical Biology 12/2002; 45(5):375-95. · 2.96 Impact Factor
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[show abstract]
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ABSTRACT: Large-scale vaccination campaigns (SIAs) and improved routine immunization (RI) have greatly reduced measles incidence in low-income countries. However, the interval between SIAs required to maintain these gains over the long term is not clear. We developed a dynamic model of measles transmission to assess measles vaccination strategies in Cambodia, Ghana, India, Morocco, Nigeria, and Uganda. We projected measles cases from 2008 to 2050 under (a) holding SIAs every 2, 4, 6, or 8 years, (b) improvements in first dose routine measles vaccine (MCV1) coverage of 0%, 1%, 3% annually, and (c) introducing MCV2 once MCV1 coverage reaches 70%, 80%, 90%. If MCV1 continues improving, then India and Nigeria could hold SIAs every 4 years without significant probability of large outbreaks, and the other countries every 6–8 years. If RI remains stagnant, India and Nigeria should hold SIAs every 2 years, and the other countries every 4–6 years.
Vaccine.
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[show abstract]
[hide abstract]
ABSTRACT: Vaccination against Hepatitis A virus (HAV) in Canada is currently targeted toward high-risk groups. However, universal vaccination has been adopted in several other countries with a similar disease burden. Here we develop an age-structured compartmental model of HAV transmission and vaccination in Canada to assess potential universal vaccination strategies. The model predicts that universal vaccination at age 1 (respectively 4, 9, 15), with phasing out of targeted vaccination, would reduce reported incidence by 60% (respectively 52, 36, 31%) and mortality attributable to HAV by 56% (respectively 45, 26, 25%), relative to continued targeted vaccination, over 80 years.
Vaccine.
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[show abstract]
[hide abstract]
ABSTRACT: Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles–Mumps–Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles–Mumps–Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice—rather than accessibility—is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.
Journal of Theoretical Biology.
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[show abstract]
[hide abstract]
ABSTRACT: Hepatitis A (HA) vaccination in Canada is currently targeted toward high-risk groups. The cost-effectiveness and expected health outcomes of universal vaccination relative to targeted vaccination in low-incidence countries such as Canada are currently unknown. Here, we conducted a cost-utility analysis for this situation, with Canada as the study population. We included vaccine costs, time costs, infection costs, and public health costs. We assessed a range of possible universal vaccination strategies over an 80-year time horizon using multiple cost perspectives. A dynamic model was used to account for herd immunity. Aggregate health gains from switching to universal vaccination are modest (10–30 QALYs per year). However, a “9 + 9” strategy that replaces two doses of monovalent hepatitis B (HB) vaccine at 9/10 years (universally administered in most provinces) with two doses of bivalent HA/HB vaccine is cost-saving from the societal perspective. At a willingness to pay threshold of $50,000/QALY, mean net benefit is +49.4 QALYs (S.D. 12.6) from the societal perspective and +3.8 QALYS (S.D. 3.0) from the payer perspective for the “9 + 9” strategy. Net benefit from the payer perspective is sensitive to the marginal cost of HA/HB vaccine relative to HB vaccine. Similar conclusions may apply in other countries with low incidence and a targeted vaccination policy.
Vaccine.
