A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity

An epidemic multi-strain model with temporary cross-immunity shows chaos, even in a previously unexpected parameter region. Especially dengue fever models with strong enhanced infectivity on secondary infection have previously shown deterministic chaos motivated by experimental findings of antibody-dependent-enhancement (ADE). Including temporary cross-immunity in such models, which is common knowledge among field researchers in dengue, we find a deterministically chaotic attractor in the more realistic parameter region of reduced infectivity on secondary infection (''inverse ADE'' parameter region). This is realistic for dengue fever since on second infection people are more likely to be hospitalized, hence do not contribute to the force of infection as much as people with first infection. Our finding has wider implications beyond dengue in any multi-strain epidemiological systems with altered infectivity upon secondary infection, since we can relax the condition of rather high infectivity on secondary infection previously required for deterministic chaos. For dengue the finding of wide ranges of chaotic attractors open new ways to analysis of existing data sets.

[1]  Pejman Rohani,et al.  Ecological and immunological determinants of dengue epidemics. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[2]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[3]  T. Monath,et al.  Dengue: the risk to developed and developing countries. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[4]  D. Ruelle.  Chaotic evolution and strange attractors , 1989 .

[5]  Yee‐Shin Lin,et al.  Immunopathogenesis of Dengue Virus Infection , 2001, Journal of Biomedical Science.

[6]  D. Gubler,et al.  Dengue and dengue haemorrhagic fever , 1998, The Lancet.

[7]  N. Ferguson,et al.  The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[9]  M. Pascual,et al.  Stochastic amplification in epidemics , 2007, Journal of The Royal Society Interface.

[10]  J. Stephenson.  Understanding dengue pathogenesis: implications for vaccine design. , 2005, Bulletin of the World Health Organization.

[11]  A. Boutayeb,et al.  A model of dengue fever , 2003, Biomedical engineering online.

[12]  Peter Schuster.  Chaotic Evolution and Strange Attractors. Von D. Ruelle. Cambridge University Press, Cambridge (UK), 1989. VIII, 96 S., Paperback £ 8.95. ‐ ISBN 0‐521‐36830‐8 , 1992 .

[13]  A J McKane,et al.  Predator-prey cycles from resonant amplification of demographic stochasticity. , 2005, Physical review letters.

[14]  Ira B Schwartz,et al.  Chaotic desynchronization of multistrain diseases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[16]  F. Takens,et al.  On the nature of turbulence , 1971 .

[17]  0 51 00 05 v 2 1 2 O ct 2 00 5 Chaotic desynchronization of multi-strain diseases , 2005 .

[18]  D. Gubler,et al.  Dengue and dengue hemorrhagic fever. , 2014 .

[19]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[20]  S. Halstead,et al.  Immune enhancement of viral infection. , 1982, Progress in allergy.

[21]  Duane J. Gubler,et al.  Dengue and Dengue Hemorrhagic Fever , 1998, Clinical Microbiology Reviews.

[22]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[23]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[24]  S. Cohen,et al.  Observations related to pathogenesis of dengue hemorrhagic fever. IV. Relation of disease severity to antibody response and virus recovered. , 1970, The Yale journal of biology and medicine.

[25]  S. Halstead,et al.  Neutralization and antibody-dependent enhancement of dengue viruses. , 2003, Advances in virus research.

[26]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[27]  Charly Favier,et al.  Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics , 2005, Proceedings of the Royal Society B: Biological Sciences.