Skip to main content
SpringerLink
Log in

Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Many infectious diseases exist as multiple variants, with interactions between variants potentially driving epidemiological dynamics. These diseases include dengue, which infects hundreds of millions of people every year and exhibits complex multi-serotype dynamics. Antibodies produced in response to primary infection by one of the four dengue serotypes can produce a period of temporary cross-immunity (TCI) to infection by other serotypes. After this period, the remaining antibodies can facilitate the entry of heterologous serotypes into target cells, thus enhancing severity of secondary infection by a heterologous serotype. This represents antibody-dependent enhancement (ADE). In this study, we analyze an epidemiological model to provide novel insights into the importance of TCI and ADE in producing cyclic outbreaks of dengue serotypes. Our analyses reveal that without TCI, such cyclic outbreaks are synchronous across serotypes and only occur when ADE produces high transmission rates. In contrast, the presence of TCI allows asynchronous cycles of serotypes by inducing a time lag between recovery from primary infection by one serotype and secondary infection by another, with such cycles able to occur without ADE. Our results suggest that TCI is a fundamental driver of asynchronous cycles of dengue serotypes and possibly other multi-variant diseases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability Statement

All data generated or analyzed during this study are included in this article and its supplementary file.

References

  • Adams B et al (2006) Cross-protective immunity can account for the alternating epidemic pattern of dengue virus serotypes circulating in Bangkok. Proc Natl Acad Sci USA 103:14234–14239

    Google Scholar 

  • Adams B, Boots M (2007) The influence of immune cross-reaction on phase structure in resonant solutions of a multi-strain seasonal SIR model. J Theor Biol 248:202–211

    MathSciNet  MATH  Google Scholar 

  • Aguiar M, Stollenwerk N (2007) A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity. arXiv:0704.3174v1

  • Aguiar M, Kooi B, Stollenwerk N (2008) Epidemiology of dengue fever: a model with temporary cross-immunity and possibly secondary infection shows bifurcations and chaotic behaviour in wide parameter regions. Math Model Nat Phenom 3:48–70

    MathSciNet  MATH  Google Scholar 

  • Aguiar M, Kooi B, Stollenwerk N (2009a) Multi-strain deterministic chaos in dengue epidemiology, a challenge for computational mathematics. AIP Conf Proc 1168:1555

    Google Scholar 

  • Aguiar M, Stollenwerk N, Kooi B (2009b) Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity. Int J Comput Math 86:1867–1877

    MathSciNet  MATH  Google Scholar 

  • Aguiar M, Ballesteros S, Kooi B, Stollenwerk N (2011) The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis. J Theor Biol 289:181–196

    MathSciNet  MATH  Google Scholar 

  • Aguiar M, Stollenwerk N, Kooi BW (2012a) Describing dengue epidemics: Insights from simple mechanistic models. AIP Conf Proc 1479:1307

    Google Scholar 

  • Aguiar M, Kooi BW, Martins J, Stollenwerk N (2012b) Scaling of stochasticity in dengue hemorrhagic fever epidemics. Math Model Nat Phenom 7:1–11

    MathSciNet  MATH  Google Scholar 

  • Aguiar M, Kooi B, Rocha F, Ghaffari P, Stollenwerk N (2013) How much complexity is needed to describe the fluctuations observed in dengue hemorrhagic fever incidence data? Ecol Complex 16:31–40

    Google Scholar 

  • Aguiar M, Paul R, Sakuntabhai A, Stollenwerk N (2014) Are we modeling the correct dataset? Minimizing false predictions for dengue fever in Thailand. Epidemiol Infect 142:2447–2459

    Google Scholar 

  • Aguiar M, Stollenwerk N, Halstead SB (2016) The impact of the newly licensed dengue vaccine in endemic countries. PLOS Negl Trop Dis 10:e0005179

    Google Scholar 

  • Aguiar M, Stollenwerk N (2017) Mathematical models of dengue fever epidemiology: multi-strain dynamics, immunological aspects associated to disease severity and vaccines. Commun Biomath Sci 1:1–12

    Google Scholar 

  • Aguiar M et al (2022) Mathematical models for dengue fever epidemiology: A 10-year systematic review. Phys Life Rev 40:65–92

    Google Scholar 

  • Altarawneh HN et al (2022) Protective effect of previous SARS-CoV-2 infection against Omicron BA.4 and BA.5 subvariants. N Engl J Med 387:1620–1622

    Google Scholar 

  • Andraud M, Hens N, Marais C, Beutels P (2012) Dengue epidemiological models for dengue transmission: A systematic review of structural approaches. PLoS ONE 7:e49085

    Google Scholar 

  • Andraud M, Hens N, Beutels P (2013) A simple periodic-forced model for dengue fitted to incidence data in Singapore. Math Biosci 244:22–28

    MathSciNet  MATH  Google Scholar 

  • Arvin AM et al (2020) A perspective on potential antibody-dependent enhancement of SARs-CoV-2. Nature 584:353–363

    Google Scholar 

  • Bartley LM, Donnelly CA, Garnett GP (2002) The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms. Trans R Soc Trop Med Hyg 96:387–397

    Google Scholar 

  • Bhatt S et al (2003) The global distribution and burden of dengue. Nature 496:504–507

    Google Scholar 

  • Bianco S, Shaw LB, Schwartz IB (2009) Epidemics with multistrain interactions: the interplay between cross immunity and antibody-dependent enhancement. Chaos 19:043123

    Google Scholar 

  • Billings L et al (2007) Instabilities in multiserotype disease models with antibody-dependent enhancement. J Theor Biol 246:18–27

    MathSciNet  MATH  Google Scholar 

  • Burattini MN et al (2008) Modelling the control strategies against dengue in Singapore. Epidemiol Infect 136:309–319

    Google Scholar 

  • Chemaitelly H et al (2022) Duration of immune protection of SARS-CoV-2 natural infection against reinfection in Qatar. J Travel Med. https://doi.org/10.1093/jtm/taac109

    Article  Google Scholar 

  • Chen Y, Cook AR, Lim AXL (2015) Randomness of dengue outbreaks on the equator. Emerg Infect Dis 21:1651–1653

    Google Scholar 

  • Coudeville L, Garnett GP (2012) Transmission dynamics of the four dengue serotypes in southern Vietnam and the potential impact of vaccination. PLoS ONE 2012:e51244

    Google Scholar 

  • Cummings DAT, Schwartz IB, Billings L, Shaw LB, Burke DS (2005) Dynamic effects of antibody-dependent enhancement on the fitness of viruses. Proc Natl Acad Sci USA 102:15259–15264

    Google Scholar 

  • Cummings DAT et al (2009) The impact of the demographic transition on dengue in Thailand: insights from a statistical analysis and mathematical modeling. PLOS Med 6:e1000139

    Google Scholar 

  • Dejnirattisai W et al (2010) Cross-reacting antibodies enhance dengue virus infection in humans. Science 328:745–748

    Google Scholar 

  • Duyen HTL et al (2011) Kinetics of plasma viremia and soluble nonstructural protein 1 concentrations in dengue: differential effects according to serotype and immune status. J Infect Dis 203:1292–1300

    Google Scholar 

  • Ferguson N, Anderson R, Gupta S (1999) The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc Natl Acad Sci USA 96:790–794

    Google Scholar 

  • Fischer DB, Halstead SB (1970) Observations related to pathogenesis of dengue hemorrhagic fever. V. Examination of agspecific sequential infection rates using a mathematical model. Yale J Biol Med 42:329–349

    Google Scholar 

  • Frank AL, Taber LH, Porter CM (1987) Influenza B virus reinfection. Am J Epidemiol 125:576–586

    Google Scholar 

  • Gibbons RV et al (2007) Analysis of repeat hospital admissions for dengue to estimate the frequency of third of fourth dengue infections resulting in admissions and dengue hemorrhagic fever, and serotype sequences. Am J Trop Med Hyg 77:910–913

    Google Scholar 

  • Gill P, Murphy A (1977) Naturally acquired immunity to influenza type A: a further prospective study. Med J Austr 2:761–765

    Google Scholar 

  • González Morales NL, Núñez-López M, Ramos-Castañeda J, Velasco-Hernández JX (2017) Transmission dynamics of two dengue serotypes with vaccination scenarios. Math Biosci 287:54–71

    MathSciNet  MATH  Google Scholar 

  • Gulbudak H, Browne CJ (2020) Infection severity across scales in multi-strain immuno-epidemiological dengue model structured by host antibody level. J Math Biol 80:1803–1843

    MathSciNet  MATH  Google Scholar 

  • Halstead SB (2014) Dengue antibody-dependent enhancement: knowns and unknowns. Microbiol Spectrum 2: AID-0022-2014

  • Hethcote HW, Stech HW, van den Driessche P (1981) Nonlinear oscillations in epidemic models. Siam J Appl Math 40:1–9

    MathSciNet  MATH  Google Scholar 

  • Hu K et al (2013) The effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever. J Theor Biol 319:62–74

    MathSciNet  MATH  Google Scholar 

  • Kabir KMA, Tanimoto J (2020) Cost-efficiency analysis of voluntary vaccination against n-serovar diseases using antibody-dependent enhancement: A game approach. J Theor Biol 503:110379

    MathSciNet  MATH  Google Scholar 

  • Kamo M, Sasaki A (2002) The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model. Physica D 165:228–241

    MATH  Google Scholar 

  • Katzelnick LC et al (2017) Antibody-dependent enhancement of severe dengue disease in humans. Science 358:929–932

    Google Scholar 

  • Knerer G, Currie CSM, Brailsford SC (2015) Impact of combined vector-control and vaccination strategies on transmission dynamics of dengue fever: a model-based analysis. Health Care Manag Sci 18:205–217

    Google Scholar 

  • Knipl D, Moghadas SM (2015) The potential impact of vaccination on the dynamics of dengue infections. Bull Math Biol 77:2212–2230

    MathSciNet  MATH  Google Scholar 

  • Kooi BW, Aguiar M, Stollenwerk N (2013) Bifurcation analysis of a family of multi-strain epidemiology models. J Comput Appl Math 252:148–158

    MathSciNet  MATH  Google Scholar 

  • Kooi BW, Aguiar M, Stollenwerk N (2014) Analysis of an asymmetric two-strain dengue model. Math Biosci 248:128–139

    MathSciNet  MATH  Google Scholar 

  • Kulkarni R (2020) Antibody-dependent enhancement of viral infections. In: Bramhachari PV (ed) Dynamics of immune activation in viral diseases. Springer Nature Singapore Pte Ltd., Singapore, pp 9–41

    Google Scholar 

  • Liu Y et al (2020) Reviewing estimates of the basic reproduction number for dengue, Zika and chikungunya across global climate zones. Environ Res 182:109114

    Google Scholar 

  • Lourenço J, Recker M (2013) Natural, persistent oscillations in a spatial multi-strain disease system with application to dengue. PLOS Comput Biol 9:e1003308

    Google Scholar 

  • Massad E et al (2008) The risk of chikungunya fever in a dengue-endemic area. J Travel Med 15:147–155

    Google Scholar 

  • Massad E, Coutinho FAB, Burattini MN (2010) A hypothesis for the 2007 dengue outbreak in Singapore. Epidemiol Infect 138:951–957

    Google Scholar 

  • McLennan-Smith TA, Mercer GN (2014) Complex behavior in a dengue model with a seasonally varying vector population. Math Biosci 238:22–30

    MATH  Google Scholar 

  • Mier-y-Teran-Romero L, Schwartz IB, Cummings DA (2013) Breaking the symmetry: Immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates. J Theor Biol 332:203–210

    MathSciNet  MATH  Google Scholar 

  • Nagao Y, Koelle K (2008) Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever. Proc Natl Acad Sci USA 105:2238–2243

    Google Scholar 

  • Nisalak A et al (2003) Serotype-specific dengue virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999. Am J Trop Med Hyg 68:191–202

    Google Scholar 

  • Pandey A, Medlock J (2015) The introduction of dengue vaccine may temporarily cause large spikes in prevalence. Epidemiol Infect 143:1276–1286

    Google Scholar 

  • Potter C, Jennings R, Nicholson K, Tyrrel D, Dickinson K (1977) Immunity to attenuated influenza virus WRL 105 infection induced by heterologous inactivated influenza A virus vaccines. J Hyg 79:321–332

    Google Scholar 

  • Rajarethinam J et al (2018) Dengue in Singapore from 2004 to 2016: cyclical epidemic patterns dominated by serotypes 1 and 2. Am J Trop Med Hyg 99:204–210

    Google Scholar 

  • Recker M et al (2009) Immunological serotype interactions and their effect on the epidemiological pattern of dengue. Proc R Soc B 276:2541–2548

    Google Scholar 

  • Rocha F, Aguiar M, Souza M, Stollenwerk N (2012) Understanding the effect of vector dynamics in epidemic models using center manifold analysis. AIP Conf Proc 1479:1319–1322

    Google Scholar 

  • Rocha F, Aguiar M, Souza M, Stollenwerk N (2013) Time-scale separation and centre manifold analysis describing vector-borne disease dynamics. Int J Comput Math 90:2105–2125

    MATH  Google Scholar 

  • Rocha F, Mateus L, Skwara U, Aguiar M, Stollenwerk N (2016) Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models. Int J Comput Math 93:1405–1422

    MathSciNet  MATH  Google Scholar 

  • Rohani P, Earn DJ, Finkenstädt B, Grenfell BT (1998) Population dynamic interference among childhood diseases. Proc R Soc B 265:2033–2041

    Google Scholar 

  • Sabin AB (1952) Research on dengue during World War II. Am J Trop Med Hyg 1:30–50

    Google Scholar 

  • Sandri M (1996) Numerical calculations of Lyapunov exponents. The Mathematica Journal 6:78–84

    Google Scholar 

  • Schwartz IB et al (2005) Chaotic desynchronization of multistrain diseases. Phys Rev 72:066201

    Google Scholar 

  • Shepard DS, Undurraga EA, Halasa YA, Stanaway JD (2016) The global economic burden of dengue: a systematic analysis. Lancet Infect Dis 16:935–941

    Google Scholar 

  • Snow GE, Haaland B, Ooi EE, Gubler DJ (2014) Review article: research on dengue during World War II revisited. Am J Trop Med Hyg 91:1203–1217

    Google Scholar 

  • St. John AL, Rathore APS (2019) Adaptive immune responses to primary and secondary dengue virus infections. Nat Rev Immunol 19:218–230

    Google Scholar 

  • Steindorf V, Kumar Srivastav A, Stollenwerk N, Kooi BW, Aguiar M (2022) Modeling secondary infections with temporary immunity and disease enhancement factor: mechanisms for complex dynamics in simple epidemiological models. Chaos Solit Fractals 164:112709

    MathSciNet  MATH  Google Scholar 

  • Stollenwerk N et al (2012) Dynamic noise, chaos and parameter estimation in population biology. Interface Focus 2:156–169

    Google Scholar 

  • Takada A, Kawaoka Y (2003) Antibody-dependent enhancement of viral infection: molecular mechanisms and in vivo implications. Rev Med Virol 13:387–398

    Google Scholar 

  • ten Bosch QA, Singh BK, Hassan MRA, Chadee DD, Michael E (2016) The role of serotype interactions and seasonality in dengue model selection and control: insights from a pattern matching approach. PLoS Negl Trop Dis 10:e0004680

    Google Scholar 

  • Tirado SMC, Yoon K-J (2003) Antibody-dependent enhancement of virus infection and disease. Viral Immunol 16:69–86

    Google Scholar 

  • Tricou V, Minh NN, Farrar J, Tran HT, Simmons CP (2011) Kinetics of viremia and NS1 antigenemia are shaped by immune status and virus serotype in adults with dengue. PLoS Negl Trop Dis 5:e1309

    Google Scholar 

  • Vuong NL et al (2021) Higher plasma viremia in the febrile phase is associated with adverse dengue outcomes irrespective of infecting serotype or host immune status: an analysis of 5642 Vietnamese cases. Clin Infect Dis 72:e1074–e1083

    Google Scholar 

  • Wearing HJ, Rohani P (2006) Ecological and immunological determinants of dengue epidemics. Proc Natl Acad Sci USA 103:11802–11807

    Google Scholar 

  • Wikramaratna PS, Simmons CP, Gupta S, Recker M (2010) The effects of tertiary and quaternary infections on the epidemiology of dengue. PLoS ONE 5:e12347

    Google Scholar 

  • Woodall H, Adams B (2014) Partial cross-enhancement in models for dengue epidemiology. J Theor Biol 351:67–73

    MathSciNet  MATH  Google Scholar 

  • World Health Organization (WHO) (2002) Global excess deaths associated with COVID-19 (modelled estimates). https://www.who.int/data/sets/global-excess-deaths-associated-with-covid-19-modelled-estimates

Download references

Acknowledgements

This work was supported by grants to R. A. Chisholm, H. E. Clapham, Natasha Howard and N. Duane Loh from Singapore’s Ministry of Education (Grant Nos. WBS A-0004771-00-00, WBS A-0004771-01-00, WBS A-0006111-00-00 and WBS A-0006111-01-00). We thank Natasha Howard, N. Duane Loh, Zhen Yuan Yeo, Deon Lum and members of Chisholm Lab at the University of Singapore for fruitful discussion of the work in this manuscript.

Author information

Authors and Affiliations

  1. Department of Biological Sciences, National University of Singapore, 16 Science Drive 4, Singapore, 117558, Singapore

    Tak Fung & Ryan A. Chisholm

  2. Saw Swee Hock School of Public Health, National University of Singapore and National University Health System, 12 Science Drive 2, Singapore, 117549, Singapore

    Hannah E. Clapham

Authors
  1. Tak Fung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hannah E. Clapham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ryan A. Chisholm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tak Fung.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 7869 kb)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fung, T., Clapham, H.E. & Chisholm, R.A. Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes. Bull Math Biol 85, 124 (2023). https://doi.org/10.1007/s11538-023-01226-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11538-023-01226-4

Keywords

Search

Navigation