A micro-epidemic model for primary dengue infection

Abstract In this paper, a micro-epidemic non-linear dynamical model has been proposed and analyzed for primary dengue infection. The model incorporates the effects of T cells immune response as well as humoral response during pathogenesis of dengue infection. The time delay has been accounted for production of antibodies from B cells. The basic reproduction number (R0) has been computed. Three equilibrium states are obtained. The existence and stability conditions for infection-free and ineffective cellular immune response state have been discussed. The conditions for existence of endemic state have been obtained. Further, the parametric region is obtained where system exhibits complex behavior. The threshold value of time delay has been computed which is critical for change in stability of endemic state. A threshold level for antibodies production rate has been obtained over which the infection will die out even though R0 > 1. The model is in line with the clinical observation that viral load decreases within 7–14 days from the onset of primary infection.

[1]  Cameron P. Simmons,et al.  Within-host viral dynamics of dengue serotype 1 infection , 2014, Journal of The Royal Society Interface.

[2]  D. Smith,et al.  Identification of GRP 78 (BiP) as a liver cell expressed receptor element for dengue virus serotype 2 , 2004, Archives of Virology.

[3]  Nuning Nuraini,et al.  Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment , 2007 .

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

[5]  H. Ansari,et al.  A With-In Host Dengue Infection Model with Immune Response and Beddington-DeAngelis Incidence Rate , 2012 .

[6]  L. Esteva,et al.  Analysis of a dengue disease transmission model. , 1998, Mathematical biosciences.

[7]  Nuning Nuraini,et al.  A with-in host Dengue infection model with immune response , 2009, Math. Comput. Model..

[8]  Katia Koelle,et al.  Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections , 2015, Journal of The Royal Society Interface.

[9]  Asep K. Supriatna,et al.  A two-age-classes dengue transmission model. , 2008, Mathematical biosciences.

[10]  Samuel Bowong,et al.  Lyapunov functions for a dengue disease transmission model , 2009 .

[11]  D. Vaughn,et al.  Dengue: an escalating problem , 2002, BMJ : British Medical Journal.

[12]  C. Janeway.  Immunobiology: The Immune System in Health and Disease , 1996 .

[13]  Duane J. Gubler,et al.  Prevention and Control of Aedes aegypti-borne Diseases: Lesson Learned from Past Successes and Failures , 2011 .

[14]  M. Nowak,et al.  Virus dynamics: Mathematical principles of immunology and virology , 2001 .

[15]  Tanvi P. Gujarati,et al.  Virus antibody dynamics in primary and secondary dengue infections , 2012, Journal of Mathematical Biology.

[16]  Sunita Gakkhar,et al.  The effects of awareness and vector control on two strains dengue dynamics , 2014, Appl. Math. Comput..

[17]  B. Murphy,et al.  Immune response to dengue virus and prospects for a vaccine. , 2011, Annual review of immunology.

[18]  M. Slifka,et al.  Contributions of humoral and cellular immunity to vaccine-induced protection in humans. , 2011, Virology.

[19]  C. Huang,et al.  Development of New Vaccines against Dengue Fever and Japanese Encephalitis , 2001, Intervirology.

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