Analysis of an SEIR-SEI four-strain epidemic dengue model with primary and secondary infections

We propose an SEIR model for the populations and an SEI model for the vector to describe the transmission dynamics of a four-strain model with both primary and secondary dengue infections. In order to accomplish this, we propose and obtain an analytic solution of a system of 47 coupled differential equations. This would be the most complete epidemic model proposed to describe the dengue epidemic.

[1]  S. Ritchie,et al.  Rapid identification of Aedes albopictus, Aedes scutellaris, and Aedes aegypti life stages using real-time polymerase chain reaction assays. , 2008, The American journal of tropical medicine and hygiene.

[2]  I. Kurane,et al.  Dengue fever and dengue haemorrhagic fever: challenges of controlling an enemy still at large , 2001, Reviews in medical virology.

[3]  Alfredo C Seijo.  El dengue como problema de salud pública , 2001 .

[4]  Filipe Rocha,et al.  How much complexity is needed to describe the fluctuations observed in dengue hemorrhagic fever incidence data , 2013 .

[5]  S. Halstead.  The XXth century dengue pandemic: need for surveillance and research. , 1992, World health statistics quarterly. Rapport trimestriel de statistiques sanitaires mondiales.

[6]  M. Guzmán,et al.  Hemorrhagic dengue in Cuba: history of an epidemic. , 1986, Bulletin of the Pan American Health Organization.

[7]  Andrei Korobeinikov,et al.  Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages , 2009, Bulletin of mathematical biology.

[8]  Delfim F. M. Torres,et al.  Vaccination models and optimal control strategies to dengue. , 2013, Mathematical biosciences.

[9]  W. Chinviriyasit,et al.  Dengue Fever with Two Strains in Thailand , 2014 .

[10]  M. Canals,et al.  [Epidemiological dynamics of Dengue on Easter Island]. , 2012, Revista chilena de infectologia : organo oficial de la Sociedad Chilena de Infectologia.

[11]  J. Hyman,et al.  The basic reproduction number R0 and effectiveness of reactive interventions during dengue epidemics: the 2002 dengue outbreak in Easter Island, Chile. , 2013, Mathematical biosciences and engineering : MBE.

[12]  Michael A. Johansson,et al.  The Incubation Periods of Dengue Viruses , 2012, PloS one.