# A Mathematical Model for Accessing Dengue Hemorrhagic Fever in Infants

## Authors

• F. A. Camargo São Paulo State University (UNESP), Rua Prof. Dr. Antônio Celso Wagner Zanin, 250, District of Rubião Júnior 18618-689, Botucatu, SP, Brazil
• T. M. Oliveira Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de biociências de Botucatu. Rua Professor Doutor Antonio Celso Wagner Zanin Unesp Campus de Botucatu 18618689 - Botucatu, SP - Brasil Telefone: (14) 38800070
• D. S. Rodrigues Universidade Estadual de Campinas, Faculdade de Tecnologia. Rua Paschoal Marmo, 1888 Jd. Nova Itália 13484332 - Limeira, SP - Brasil Telefone: (19) 21133474
• P. F. A. Mancera São Paulo State University (UNESP), Rua Prof. Dr. Antônio Celso Wagner Zanin, 250, District of Rubião Júnior 18618-689, Botucatu, SP, Brazil
• F. L. P. Santos São Paulo State University (UNESP), Rua Prof. Dr. Antônio Celso Wagner Zanin, 250, District of Rubião Júnior 18618-689, Botucatu, SP, Brazil

## Keywords:

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

## Abstract

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.

## Author Biography

### F. A. Camargo, São Paulo State University (UNESP), Rua Prof. Dr. Antônio Celso Wagner Zanin, 250, District of Rubião Júnior 18618-689, Botucatu, SP, Brazil

Postgraduate Program in Biometrics, Institute of Biosciences, campus Botucatu.

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2022-03-25

## How to Cite

Camargo, F. A., Oliveira, T. M., Rodrigues, D. S., Mancera, P. F. A., & Santos, F. L. P. (2022). A Mathematical Model for Accessing Dengue Hemorrhagic Fever in Infants. Trends in Computational and Applied Mathematics, 23(1), 101–115. https://doi.org/10.5540/tcam.2022.023.01.00101

Original Article