Instabilities in multiserotype disease models with antibody-dependent enhancement

Billings, Lora; Schwartz, Ira B.; Shaw, Leah B.; McCrary, Marie; Burke, Donald S.; Cummings, Derek A. T.

doi:10.1016/j.jtbi.2006.12.023

Cited by 52 publications

(58 citation statements)

References 16 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Wavelet software was provided by C. Torrence and G. Compo and is available at http://paos.colorado.edu/research/ wavelets. model assumes that immunity to reinfection with a previously experienced serotype is permanent, consistent with empirical data (3), and in agreement with previous mathematical models of dengue (28)(29)(30)(31)(32). On the basis of findings from epidemiological studies, we also assume that the risk of developing DHF is higher in secondary (or later) infections than in primary infections; we consider this increased risk to be the sole effect of ADE, in contrast to previous models wherein ADE is assumed to enhance either susceptibility to reinfection with a heterologous serotype (28,33,34), an infected individual's transmissibility (30,31,34), or a host's mortality (34,35).…”

Section: Resultssupporting

confidence: 83%

Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever

Nagao

Koelle

2008

Proc. Natl. Acad. Sci. U.S.A.

148

173

View full text Add to dashboard Cite

Dengue hemorrhagic fever (DHF) is a potentially fatal manifestation of an infection with the mosquito-borne dengue virus. Because of the social and economic costs of DHF, many countries in Asia and South America have initiated public health measures aimed at vector control. Despite these measures, DHF incidence rates do not appear to be declining. The effectiveness of vector control in reducing dengue transmissibility has thereby been questioned. Here, we revisit this conclusion using epidemiological data from Thailand. We first show, with age incidence data, that dengue transmission rates have fallen since 1981; surprisingly, however, these declines are not associated with decreases in DHF incidence. Instead, district-level analyses indicate a nonmonotonic relationship between the basic reproductive number R 0 and DHF incidence. To understand this relationship, we formulated three mathematical models, which differ in their assumptions of transient between-serotype cross-protection. Unlike the first two models, the previously unconsidered third model with clinical cross-protection can reproduce this nonmonotonic relationship. Simulation of this model with nonstationary R 0 reproduces several previously unexplained patterns of dengue dynamics, including a transition from a Ϸ2-year cycle to a Ϸ4-year cycle and a transient trough in DHF incidence in provinces with rapid R 0 declines. These results imply that DHF incidence can be effectively controlled with a sufficiently large reduction in R 0 but that moderate reductions may be counterproductive. More broadly, these results show that assuming parameter stationarity in systems with approximate stationarity in disease incidence is unjustified and may result in missed opportunities to understand the drivers of disease variability.dengue dynamics ͉ interannual disease variability ͉ multistrain dynamics

show abstract

Section: Resultssupporting

confidence: 83%

Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever

Nagao

Koelle

2008

Proc. Natl. Acad. Sci. U.S.A.

148

173

View full text Add to dashboard Cite

show abstract

“…We observe a chaotic window for φ < 1 where this dynamical behaviour has never been described before, and also another one for φ > 1, where the minimal values go to very low numbers of infected, the classical "ADE chaotic region", which already has been described in previous publications [13,30,6].…”

Section: Numerical Bifurcation Diagramsupporting

confidence: 75%

“…More recently, modelling attention has focussed on higher viral load of hosts on secondary infection than on the first due to ADE, hence a higher contribution to the force of infection of each strain, reporting deterministically chaotic attractors [13] and chaos desynchronization [30,6] to explain the co-existence of the known four dengue viral strains. Temporary cross-immunity against all strains after a first infection has been included in mathematical models as well, but again limiting the effect of ADE to increase the contribution of secondary cases to the force of infection [33].…”

Section: Introductionmentioning

confidence: 99%

Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions

Aguiar

Kooi

Stollenwerk

2008

Math. Model. Nat. Phenom.

132

View full text Add to dashboard Cite

Abstract. Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers in dengue, we find bifurcations up to chaotic attractors in much wider and also unexpected parameter regions of reduced infectivity on secondary infection, realistically describing more likely hospitalization on secondary infection when the viral load becomes high. The model shows Hopf bifurcations, symmetry breaking bifurcations of limit cycles, coexisting isolas, and two different possible routes to chaos, via the Feigenbaum period doubling and via torus bifurcations.

show abstract

“…In the literature the multi-strain interaction leading to deterministic chaos via ADE has been described previously, e.g. (Billings et al, 2007;Ferguson et al, 1999;Schwartz et al, 2005) (Aguiar & Stollenwerk, 2007;Aguiar et al, 2008Aguiar et al, , 2009 by including temporary cross immunity into dengue models with ADE, a rich dynamic structure including deterministic chaos was found in wider and more biologically realistic parameter regions.…”

Section: Dengue Fever Epidemiologymentioning

confidence: 88%

“…Dengue models including multi-strain interactions via ADE but without temporary cross immunity period e.g. (Billings et al, 2007;Ferguson et al, 1999;Schwartz et al, 2005) have shown deterministic chaos when strong infectivity on secondary infection was assumed. The addition of the temporary cross immunity period in such models shows a new chaotic attractor in an unexpected parameter region of reduced infectivity on secondary infection (Aguiar & Stollenwerk, 2007;Aguiar et al, 2008Aguiar et al, , 2009, i.e.…”

Section: Multi-strain Models Motivated By Dengue Fever Epidemiology: mentioning

confidence: 99%

Modeling Infectious Diseases Dynamics: Dengue Fever, a Case Study

Aguiar¹,

Stollenwerk²,

Kooi³

2012

Epidemiology Insights

View full text Add to dashboard Cite

Instabilities in multiserotype disease models with antibody-dependent enhancement

Cited by 52 publications

References 16 publications

Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever

Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever

Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions

Modeling Infectious Diseases Dynamics: Dengue Fever, a Case Study

Contact Info

Product

Resources

About