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The effects of tertiary and quaternary infections on the epidemiology of dengue.

Wikramaratna PS, Simmons CP, Gupta S, Recker M - PLoS ONE (2010)

Bottom Line: The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes.Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion.Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Oxford, Oxford, United Kingdom.

ABSTRACT
The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes. Whilst infection by one serotype appears to convey life-long protection to homologous infection, it is believed to be a risk factor for severe disease manifestations upon secondary, heterologous infection due to the phenomenon of Antibody-Dependent Enhancement (ADE). Subsequent clinical infections are rarely reported and, since the majority of dengue infections are generally asymptomatic, it is not clear if and to what degree tertiary or quaternary infections contribute to dengue epidemiology. Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion. More importantly, permitting third and fourth infections significantly increases the force of infection without resorting to high basic reproductive numbers. Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

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Related in: MedlinePlus

Comparison of age structured dynamics between model (i) and model (ii).(a) The lines show the proportion of the population at each age (for model (i) (top) and model (ii) (bottom)) who have suffered one (solid dark blue line), two (solid red), three (solid green), four (solid magenta) and any (solid black) dengue infections. For model (ii) the proportion of the population that is at risk of disease (defined as having seen 1, 2 or 3 serotypes) is also plotted (dotted black) for comparison to the equivalent in model (i) (solid dark blue). Generally, in model (ii) people are exposed to dengue at an earlier age, experience heterologous infections younger, and take much longer to become completely immune. (b) For model (i) ((ii)), the blue (green) bar shows how the average age of disease (DHF), determined as heterologous infection, changes with the number of serotypes present whilst the small bars show the change in age of first infection. The increase in the total force of infection with the number of serotypes is shown as dotted lines (model (i): blue, and model (ii): green). (c) For model (i) (blue line) and model (ii) (green line) we observe that increasing  acts to decrease the average age of first infection (here estimated as 1/total force of infection) and that for all levels of  this value is significantly lower when allowing for third and fourth infection (model (ii)). Parameter values:  ((a), (b) and (c)) and  (a),  (b).
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pone-0012347-g005: Comparison of age structured dynamics between model (i) and model (ii).(a) The lines show the proportion of the population at each age (for model (i) (top) and model (ii) (bottom)) who have suffered one (solid dark blue line), two (solid red), three (solid green), four (solid magenta) and any (solid black) dengue infections. For model (ii) the proportion of the population that is at risk of disease (defined as having seen 1, 2 or 3 serotypes) is also plotted (dotted black) for comparison to the equivalent in model (i) (solid dark blue). Generally, in model (ii) people are exposed to dengue at an earlier age, experience heterologous infections younger, and take much longer to become completely immune. (b) For model (i) ((ii)), the blue (green) bar shows how the average age of disease (DHF), determined as heterologous infection, changes with the number of serotypes present whilst the small bars show the change in age of first infection. The increase in the total force of infection with the number of serotypes is shown as dotted lines (model (i): blue, and model (ii): green). (c) For model (i) (blue line) and model (ii) (green line) we observe that increasing acts to decrease the average age of first infection (here estimated as 1/total force of infection) and that for all levels of this value is significantly lower when allowing for third and fourth infection (model (ii)). Parameter values: ((a), (b) and (c)) and (a), (b).

Mentions: The only notable effect of third and fourth infections, so far, has been an overall higher propensity for desynchronised, large amplitude oscillations. This, however, can be directly attributed to an overall higher level of transmission that is achieved and maintained by a larger proportion of the population susceptible to infection and onward transmission. We therefore also expect an effect on age-structured prevalence and incidence rates. To explicitly compare the age structure of prevalence within each model we adapted the methods of [21]. We consider in both models the distinct (unstable) equilibrium solutions where all strains have equal forces of infection in the case of medium levels of enhancement (). This equilibrium serves as an approximation of the mean prevalence of each serotype over a long period of time. In this case, the proportion of the population that has experienced exactly ā€˜iā€™ different strains is given by . The probability of acquiring a new infection is then proportionate to the number of yet un-encountered strains. In this case with four co-circulating dengue serotypes individuals enter from at a rate , where is the average per capita force of infection per strain. The dynamics of this system with respect to time, , and age, , may then be described by the following set of partial differential equations for :where the proportion of individuals yet unexposed is given by . We can then solve these equations (noting, in this instance, that the time derivative is zero) to approximate how the number of infections varies with age in each model. In Figure 5a we have then plotted this data for each model in order to compare and contrast age structures. In Figure 5b we have made a minor adaptation to the models in that we consider the case of just 2 or 3 co-circulating serotypes of dengue. To generate this figure we repeated the above and show how the age of first infection, average age of disease and total force of infection changes for each scenario in both models. Finally, Figure 5c shows how the average age of first infection changes with increasing in both of our models.


The effects of tertiary and quaternary infections on the epidemiology of dengue.

Wikramaratna PS, Simmons CP, Gupta S, Recker M - PLoS ONE (2010)

Comparison of age structured dynamics between model (i) and model (ii).(a) The lines show the proportion of the population at each age (for model (i) (top) and model (ii) (bottom)) who have suffered one (solid dark blue line), two (solid red), three (solid green), four (solid magenta) and any (solid black) dengue infections. For model (ii) the proportion of the population that is at risk of disease (defined as having seen 1, 2 or 3 serotypes) is also plotted (dotted black) for comparison to the equivalent in model (i) (solid dark blue). Generally, in model (ii) people are exposed to dengue at an earlier age, experience heterologous infections younger, and take much longer to become completely immune. (b) For model (i) ((ii)), the blue (green) bar shows how the average age of disease (DHF), determined as heterologous infection, changes with the number of serotypes present whilst the small bars show the change in age of first infection. The increase in the total force of infection with the number of serotypes is shown as dotted lines (model (i): blue, and model (ii): green). (c) For model (i) (blue line) and model (ii) (green line) we observe that increasing  acts to decrease the average age of first infection (here estimated as 1/total force of infection) and that for all levels of  this value is significantly lower when allowing for third and fourth infection (model (ii)). Parameter values:  ((a), (b) and (c)) and  (a),  (b).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2925950&req=5

pone-0012347-g005: Comparison of age structured dynamics between model (i) and model (ii).(a) The lines show the proportion of the population at each age (for model (i) (top) and model (ii) (bottom)) who have suffered one (solid dark blue line), two (solid red), three (solid green), four (solid magenta) and any (solid black) dengue infections. For model (ii) the proportion of the population that is at risk of disease (defined as having seen 1, 2 or 3 serotypes) is also plotted (dotted black) for comparison to the equivalent in model (i) (solid dark blue). Generally, in model (ii) people are exposed to dengue at an earlier age, experience heterologous infections younger, and take much longer to become completely immune. (b) For model (i) ((ii)), the blue (green) bar shows how the average age of disease (DHF), determined as heterologous infection, changes with the number of serotypes present whilst the small bars show the change in age of first infection. The increase in the total force of infection with the number of serotypes is shown as dotted lines (model (i): blue, and model (ii): green). (c) For model (i) (blue line) and model (ii) (green line) we observe that increasing acts to decrease the average age of first infection (here estimated as 1/total force of infection) and that for all levels of this value is significantly lower when allowing for third and fourth infection (model (ii)). Parameter values: ((a), (b) and (c)) and (a), (b).
Mentions: The only notable effect of third and fourth infections, so far, has been an overall higher propensity for desynchronised, large amplitude oscillations. This, however, can be directly attributed to an overall higher level of transmission that is achieved and maintained by a larger proportion of the population susceptible to infection and onward transmission. We therefore also expect an effect on age-structured prevalence and incidence rates. To explicitly compare the age structure of prevalence within each model we adapted the methods of [21]. We consider in both models the distinct (unstable) equilibrium solutions where all strains have equal forces of infection in the case of medium levels of enhancement (). This equilibrium serves as an approximation of the mean prevalence of each serotype over a long period of time. In this case, the proportion of the population that has experienced exactly ā€˜iā€™ different strains is given by . The probability of acquiring a new infection is then proportionate to the number of yet un-encountered strains. In this case with four co-circulating dengue serotypes individuals enter from at a rate , where is the average per capita force of infection per strain. The dynamics of this system with respect to time, , and age, , may then be described by the following set of partial differential equations for :where the proportion of individuals yet unexposed is given by . We can then solve these equations (noting, in this instance, that the time derivative is zero) to approximate how the number of infections varies with age in each model. In Figure 5a we have then plotted this data for each model in order to compare and contrast age structures. In Figure 5b we have made a minor adaptation to the models in that we consider the case of just 2 or 3 co-circulating serotypes of dengue. To generate this figure we repeated the above and show how the age of first infection, average age of disease and total force of infection changes for each scenario in both models. Finally, Figure 5c shows how the average age of first infection changes with increasing in both of our models.

Bottom Line: The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes.Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion.Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Oxford, Oxford, United Kingdom.

ABSTRACT
The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes. Whilst infection by one serotype appears to convey life-long protection to homologous infection, it is believed to be a risk factor for severe disease manifestations upon secondary, heterologous infection due to the phenomenon of Antibody-Dependent Enhancement (ADE). Subsequent clinical infections are rarely reported and, since the majority of dengue infections are generally asymptomatic, it is not clear if and to what degree tertiary or quaternary infections contribute to dengue epidemiology. Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion. More importantly, permitting third and fourth infections significantly increases the force of infection without resorting to high basic reproductive numbers. Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

Show MeSH
Related in: MedlinePlus