THEORETICAL STUDY OF THE MATHEMATICAL MODEL ON THE POPULATION DYNAMICS OF DENGUE

Authors

  • R. U. Akhaze Department of Mathematics, University of Benin, Benin City, Nigeria. Author
  • I. I. Ako Department of Mathematics, University of Benin, Benin City, Nigeria. Author
  • O. O. Olowo Department of Mathematics, University of Benin, Benin City, Nigeria. Author

Keywords:

antibody-dependent enhancement (ADE), cross-immunity (CI), co-circulating, infective, dengue disease, epidemic, disease-free equilibrium, Basic reproduction number

Abstract

We present a deterministic nonlinear mathematical model describing the population dynamics of Dengue which provides public health insights to the impact of dual infectivity of an Aedes aegypti with two strains of dengue, where both strains are co-circulating with cross-immunity (CI) and antibody-dependent enhancement (ADE) in the course of the dynamics of the disease. The model is rigorously analyzed qualitatively and thresholds for eradication are established.

         Views | Downloads: 52 / 12

Downloads

Download data is not yet available.

References

S.V. Mayer, R.B. Tesh, N. Vasilakis (2017). The emergence of arthropod borne viral diseases: A global prospective on dengue, chikungunya and Zika fever. Vol.166: 155-163.

Dejinirahisai, Noisakran, S., Onloimoon, N., Songprakhan, P., Hsiao, H., Chokephaibulkit, K. and Perng, G.C. (2010). Cells in Dengue virus infection in vivo, Advance in virology, (2010), Article ID 164878, 15 pages.

Schmid, M.A., Diamond, M.S. and Harris, E. (2014). Dendritic cells in dengue virus infection: targets of virus replication and mediators of immunity. https://doi.org 10.3389.

Nature Publishing Group (N.P.G) (2003). Adapted from Diamond, M. S. Evasion of innate and adaptive immunity by flaviviruses. Immunology and Cell Biology 81, 196--206.

Colpitts T.M. (2012). West Nile virus: Biology Transmission and Haman infection.

Nishiura, H., and Halstead, S.B. (2007). Natural History of Dengue virus (DENV)-1 and (DENV)-4 Infections: Reanalysis of classic studies.

Normile, D. (2013). Tropical Medicine surprising new dengue virus throws a spanner in disease control efforts. PubMed.

Gubler, D.J., Lambrechts, L. and Scott, T.W. (2010). Consequences of the expanding global distribution of {Aedes albopictus} for dengue virus transmission.

Bancroft, T.L. (1906). On the etiology of dengue fever.

Garba, S. M. and Gumel, A. B. (2010). Effect of cross-immunity on the transmission dynamics of two strains of dengue, International Journal of Computer Mathematics, 87:10.

Kalayanarooj, S. (2011). Clinical manifestation and management of Dengue/DHF/DSS.

Gurugama, P., Garg, P., Perera, J., Wijewickrama, A. and Seneviratne, S.L. (2010). Dengue viral infections.

Halstead, S.B. (2014). Dengue Antibody-Dependent Enhancement: knows and unknowns.

World Health Organization (W.H.O) (1986). Dengue haemorrhagic fever: diagnosis, treatment, prevention and control.

Nature Publishing Group (N.P.G) (2007). Dengue retinopathy, manifesting with bilateral vasculitis and macular.

Dejinirahisai, Noisakran, S., Onloimoon, N., Songprakhan, P., Hsiao, H., Chokephaibulkit, K. and Perng, G.C. (2010). Cells in Dengue virus infection in vivo, Advance in virology, (2010), Article ID 164878, 15 pages.

Espinoza-Gomez, F., Delgado-Enciso, I., Valle-Reyes, S., Ochoa-Jimenez, R., Arechiga-Ramiraz, C., Gamez- Arroyo, J. L., Vazquez-Campuzano, R., Guzman-Bracho, C., Vasquez, C. and Lopez-lemus, U.A. (2017). Dengue virus co-infection in Human immunodeficiency virus-1-infected patients on the West Coast of Mexico.

Li-pat-Yuen G. (2015). Simultaneous detection of chikungunya virus, and human dengue pathogenic leptospira genomesusing a multiplex TaqMan.

Dumont, Y. and Chiroleu, F. (2010), Vector control for the chikungunya disease. Mathematical Biosciences and Engineering, 7:105-111.

Transactions of the Nigerian Association of Mathematical Physics Volume 17, (Oct. – Dec., 2021), 67 –82

Akhaze, Ako and Olowo Trans. Of NAMP Okuneye, O.O. and Gumel, A.B. (2016). Analysis of a Temperature and Rainfall Dependent Model for Malaria Transmission Dynamics}, Mathematical Biosciences. DOI: 10.1016/j.mbs.2016.03.013, 2015. Lakshmikantham, V. (1991). Stability analysis of nonlinear systems, {SIAM Review} 33(1): 152- 154.

Van den Driessche and watmough, J. (2002). ‘Reproduction numbers and sub-theshold endemic equilibria for compartmental models of disease transmission mathematical Biosciences vol.180.

Carlos Castillo-Chavez and Baojun Song (2004). Dynamical models of Tuberculosis and their Applications based on center manifold theory. Mathematical Biosciences and Engineering. MBE 1(2):361-404.N/ BN/

Downloads

Published

2021-12-01

How to Cite

THEORETICAL STUDY OF THE MATHEMATICAL MODEL ON THE POPULATION DYNAMICS OF DENGUE. (2021). The Transactions of the Nigerian Association of Mathematical Physics, 17, 67 –82. https://nampjournals.org.ng/index.php/tnamp/article/view/208

Share

Similar Articles

1-10 of 42

You may also start an advanced similarity search for this article.