A Mathematical Model for Accessing Dengue Hemorrhagic Fever in Infants

F. A. Camargo, T. M. Oliveira, D. S. Rodrigues, P. F. A. Mancera, F. L. P. Santos


A mathematical model was developed to describe the dynamics of the primary infection of dengue virus in infant who were born of a mother immune to some serotype of the dengue virus. The model is given by a system of nonlinear ordinary differential equations with the time-dependent variables for the number of DENV antibodies of the infant transferred from their immune, uninfected and infected monocytes and dengue virus. The mathematical analysis was carried out where the conditions for the existence of the disease-free equilibrium and the endemic equilibrium were established. The numerical simulations were performed considering different scenarios for R0 (Basic Reproductive Number), illustrating the global convergence of the numerical results for the equilibrium points. The results are in agreement with our derived global stability analysis. It can be concluded that the DHF in the infants could occur in the peaks observed for the infected monocytes and dengue virus.


system of differential equations; global analysis; virus; infant; numerical simulations

Full Text:



W. H. Organization, "Dengue and severe dengue," 2017, http://apps.who.int/mediacentre/factsheets/fs117/en/index.html, Accessed: 2019-01-07.

M. G. Guzman, M. Alvarez, and S. B. Halstead, "Secondary infection as a risk factor for dengue hemorrhagic fever/dengue shock syndrome: an historical perspective and role of antibody-dependent enhancement of infection," Archives of virology, vol. 158, no. 7, pp. 1445-1459, 2013.

P. Palmeira, C. Quinello, A. L. Silveira-Lessa, C. A. Zago, and M. Carneiro-Sampaio, "Igg placental transfer in healthy and pathological pregnancies," Clinical and Developmental Immunology, vol. 2012, 2011.

P. M. Castanha, C. Braga, M. T. Cordeiro, A. I. Souza, C. D. Silva Jr, C. M. Martelli, W. G. van Panhuis, E. J. Nascimento, and E. T. Marques, "Placental transfer of dengue virus (denv)-specific antibodies and kinetics of denv infection-enhancing activity in brazilian infants," The Journal of Infectious Diseases, vol. 214, no. 2, pp. 265-272, 2016.

R. Nikin-Beers and S. M. Ciupe, "The role of antibody in enhancing dengue virus infection," Mathematical Biosciences, vol. 263, pp. 83-92, 2015.

S. L. Maroun, R. C. Marliere, R. C. Barcellus, C. N. Barbosa, J. R. Ramos, M. E. Moreira, et al., "Relato de caso: transmissão vertical de dengue," 2008.

A. Jain and U. C. Chaturvedi, "Dengue in infants: an overview," FEMS Immunology & Medical Microbiology, vol. 59, no. 2, pp. 119-130, 2010.

S. B. Halstead, N. T. Lan, T. T. Myint, T. N. Shwe, A. Nisalak, S. Kalyanarooj, S. Nimmannitya, S. Soegijanto, D. W. Vaughn, and T. P. Endy, "Dengue hemorrhagic fever in infants: research opportunities ignored," Emerging Infectious Diseases, vol. 8, no. 12, p. 1474, 2002.

Z. Kou, J. Y. Lim, M. Beltramello, M. Quinn, H. Chen, S.-n. Liu, L. Martnez-Sobrido, M. S. Diamond, J. J. Schlesinger, A. de Silva, et al., "Human antibodies

against dengue enhance dengue viral infectivity without suppressing type i interferon secretion in primary human monocytes," Virology, vol. 410, no. 1, pp. 240-247, 2011.

R. P. Duffin and R. H. Tullis, Mathematical models of the complete course of hiv infection and aids," Computational and Mathematical Methods in Medicine, vol. 4, no. 4, pp. 215-221, 2002.

J. A. Mosquera, J. P. Hernandez, N. Valero, L. M. Espina, and G. J. Añez, "Ultrastructural studies on dengue virus type 2 infection of cultured human monocytes," Virology Journal, vol. 2, no. 1, p. 26, 2005.

J. Zalevsky, A. K. Chamberlain, H. M. Horton, S. Karki, I. W. Leung, T. J. Sproule, G. A. Lazar, D. C. Roopenian, and J. R. Desjarlais, "Enhanced antibody half-life improves in vivo activity," Nature Biotechnology, vol. 28, no. 2, p. 157, 2010.

M. Martcheva, An introduction to mathematical epidemiology, vol. 61. Springer, 2015.

Z. Shuai and P. van den Driessche, "Global stability of infectious disease models using lyapunov functions," SIAM Journal on Applied Mathematics, vol. 73, no. 4, pp. 1513-1532, 2013.

C. Vargas-De-León, "On the global stability of sis, sir and sirs epidemic models with standard incidence," Chaos, Solitons & Fractals, vol. 44, no. 12, pp. 1106-1110, 2011.

S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, "A methodology for performing global uncertainty and sensitivity analysis in systems biology," Journal of Theoretical Biology, vol. 254, no. 1, pp. 178-196, 2008.

DOI: https://doi.org/10.5540/tcam.2022.023.01.00101

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:




Desenvolvido por:

Logomarca da Lepidus Tecnologia