Patches Approach to Investigate the Populational Dynamics in Dengue

Fernando Luiz Pio Santos

Abstract


In areas where resources are located in patches or discrete locations, human dispersal is more conveniently modeled, in which the population is divided into discrete patches. In this work we develop a general discrete model to analyze the spread of Dengue disease. In the process of mathematical modeling we take into account the human populations and the circulation of a single serotype of dengue mosquitoes. The movements of susceptible, infected and recovered humans among all patches are considered. Aquatic phases with different carrying capacities are considered within the patches. Also an arbitrary number of patches can be used to simulate the spread of dengue disease. In this paper we performed numerical experiments to show the applicability of this methodology to investigate the dengue disease problem. The general discrete space model was developed for solving epidemiological problems whereas the human-vector interactions and human mobilities play an important role. Based on our numerical results, we may recommend the general patches model for solving epidemiological problems in Population Dynamics. 


Keywords


Human dispersal, Discrete model, Pathway approach, ODE system, Euler method, Dynamic Population.

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DOI: http://dx.doi.org/10.5540/tema.2017.018.01.0003

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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