Epidemics with multistrain interactions: the interplay between cross immunity and antibody-dependent enhancement.

This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in multistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, strong cross immunity is shown numerically to cause oscillations and chaotic outbreaks even for low values of ADE.

[1]  S. Halstead,et al.  Antibody-enhanced dengue virus infection in primate leukocytes , 1977, Nature.

[2]  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.

[3]  Donald S Burke,et al.  Serotype-specific dengue virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999. , 2003, The American journal of tropical medicine and hygiene.

[4]  Thomas F. Fairgrieve,et al.  AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) , 1997 .

[5]  Simon A. Levin,et al.  The dynamics of cocirculating influenza strains conferring partial cross-immunity , 1997, Journal of mathematical biology.

[6]  Katia Koelle,et al.  Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever , 2008, Proceedings of the National Academy of Sciences.

[7]  Ira B Schwartz,et al.  Dynamic effects of antibody-dependent enhancement on the fitness of viruses. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Laith J. Abu-Raddad,et al.  The impact of cross-immunity, mutation and stochastic extinction on pathogen diversity , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  Tom Starzl,et al.  THE LANCET , 1992, The Lancet.

[10]  Akira Sasaki,et al.  The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model , 2002 .

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

[12]  Carlos Castillo-Chavez,et al.  Dynamics of Two-Strain Influenza with Isolation and Partial Cross-Immunity , 2005, SIAM J. Appl. Math..

[13]  Akira Sasaki,et al.  Cross-immunity, invasion and coexistence of pathogen strains in epidemiological models with one-dimensional antigenic space. , 2007, Mathematical biosciences.

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

[15]  B. Guy,et al.  Towards a dengue vaccine: progress to date and remaining challenges. , 2008, Comparative immunology, microbiology and infectious diseases.

[16]  D. Gubler,et al.  Viraemia in patients with naturally acquired dengue infection. , 1981, Bulletin of the World Health Organization.

[17]  M. Golubitsky,et al.  Hopf Bifurcation in the presence of symmetry , 1984 .

[18]  Akira Sasaki,et al.  Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[19]  A. Sabin.  Research on dengue during World War II. , 1952, The American journal of tropical medicine and hygiene.

[20]  Ira B Schwartz,et al.  Instabilities in multiserotype disease models with antibody-dependent enhancement. , 2007, Journal of theoretical biology.

[21]  Lourdes Esteva,et al.  Coexistence of different serotypes of dengue virus , 2003, Journal of mathematical biology.

[22]  M. Golubitsky,et al.  Hopf Bifurcation in the presence of symmetry , 1985 .

[23]  Nico Stollenwerk,et al.  A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity , 2007, 0704.3174.

[24]  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.

[25]  I. Schwartz,et al.  Using dimension reduction to improve outbreak predictability of multistrain diseases , 2006, Journal of mathematical biology.

[26]  Lam Sk,et al.  Dengue and dengue hemorrhagic fever. , 1990 .

[27]  S. Halstead,et al.  The future of dengue vaccines , 2002, The Lancet.

[28]  Ben Adams,et al.  Modelling the relationship between antibody-dependent enhancement and immunological distance with application to dengue. , 2006, Journal of theoretical biology.

[29]  D. Gubler.  Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century. , 2002, Trends in microbiology.

[30]  E. C. Holmes,et al.  Cross-protective immunity can account for the alternating epidemic pattern of dengue virus serotypes circulating in Bangkok , 2006, Proceedings of the National Academy of Sciences.

[31]  N. Ferguson,et al.  Chaos, persistence, and evolution of strain structure in antigenically diverse infectious agents. , 1998, Science.

[32]  N M Ferguson,et al.  Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[33]  Charles H. Hoke,et al.  SEROTYPE-SPECIFIC DENGUE VIRUS CIRCULATION AND DENGUE DISEASE IN BANGKOK, THAILAND FROM 1973 TO 1999 , 2003 .