Applied and Computational Mathematics
Volume 5, Issue 4, August 2016, Pages: 169-176
Received: Jun. 14, 2016;
Accepted: Jul. 18, 2016;
Published: Aug. 3, 2016
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Bentara Wadu Mesthrige Nadi Madushani De Silva, Department of Mathematics, University of Colombo, Colombo, Sri Lanka
Shyam Sanjeewa Nishantha Perera, Department of Mathematics, University of Colombo, Colombo, Sri Lanka
Naleen Chaminda Ganegoda, Department of Mathematics, University of Sri Jayewardenepura, Nugegoda, Sri Lanka
Dengue is one of the most prevalent viruses transmitted by mosquitoes where increasing incidence and severity claim severe social burden. This virus is common throughout the tropics and subtropics. Dengue is a virus which propagated during the day and thus the mobility of humans can cause it to spread quickly. In this paper, we introduce mobility of humans between two neighboring areas into a mathematical model for the transmission of dengue. Dengue transmission is modeled using the classical SIR model. Simulations have been carried under four cases to compare the impact of human mobility to propagate the dengue disease. These cases are based on existence of dengue and human mobility direction regarding neighboring area. Numerical simulations are carried out using Matlab routine ode 45.
Bentara Wadu Mesthrige Nadi Madushani De Silva,
Shyam Sanjeewa Nishantha Perera,
Naleen Chaminda Ganegoda,
Modeling the Effect of Human Mobility on Dengue Transmission, Applied and Computational Mathematics.
Vol. 5, No. 4,
2016, pp. 169-176.
Boston College, Biology Department, Dengue, (2014, July 8), Retrieved from http://www.bc.edu/schools/cas/biology/research/infect/dengue.html.
M. Derouich, and A. Boutayeb, “Dengue fever: Mathematical Modeling and Computer Simulation,” Applied Mathematics and Computation, vol. 177, No 2, 2006, pp 528-544.
P. Puntani, “Transmission Model for Dengue Disease with and without the Effect of Extrinsic Incubation Period,” KMITL Sci. Tech. J., vol. 6, No 2, 2006, pp 74-82.
M. Derouich, A. Boutayeb, and E. H. Twizell, “A model of dengue fever,” BioMedical Engineering OnLine, vol. 2, No 4, 2003, pp 1-10.
National Institute for Allergy and Infectious Disease, Dengue Fever, (2014, July 8), Retrieved from http://www.niaid.nih.gov/topics/DengueFever/Research/BasicResearch/pages/howdenguematures.aspx
M. Choisy, J. F. Guegan and P. Rohani, “Mathematical Modeling of infectious Diseases Dynamics,” Encyclopedia of infectious Diseases: Modern Methodologies.
R. Sinden, “Malaria, Mosquitoes and the Legacy of Ronald Ross,” Bull World Health Organ, vol. 85, No. 11, 2007, pp 894-896.
S. T. R. Pinho, C. P. Ferreira, L. Esteva, F. R. Barreto, V. C. Morato e Silva and M. G. L. Teixeria, “Modelling the Dynamics of Dengue Real Epidemics,” Philosophical Transactions of the Royal Society A, vol. 368, 2010, pp 5679-5693.
L. B. L. Santos, M. C. Costa, S. T. R. Pinho, R. F. S. Andrade, F. R. Barreto, M. G. Teixeira and M. L. Barreto, “Periodic Forcing in a Three-Level Cellular Automata Model for a Vector-Transmitted Disease,” Physical. Review. E, vol. 80, 2009, pp 016102-016109.
H. M. Yang, and C. P. Ferrerira, “Assessing the Effects Vector Control on Dengue Transmission,” Applied Mathematics and Computation, vol. 198, 2008, pp 401-413.
N. A. Maidana, and H. M. Yang, “Describing the Geographic Spread of Dengue Disease by Traveling Waves,” Mathematical Biosciences, vol. 215, 2008, pp 64-77.
History of Dengue, (2016), Dengue Virus Net, http://www.Denguevirusnet.com/history-of-Dengue.html.
Dengue and Severe dengue, (2016, April), WHO, http://www.who.int/mediacentre/factsheets/fs117/en/.
W. P. T. M. Wickrmaarachchi, S. S. N. Perera, S. Jayasinghe, and P. Kariyawasam, “The influence of the human mobility for dengue disease transmission in Urban Colombo and bordering areas of Colombo: A cross wavelet approach,” International Conference of Eastern University Sri Lanka, 2013, pp 24.
W. P. T. M. Wickrmaarachchi, S. S. N. Perera, S. Jayasinghe, P. Kariyawasam, and P. Kariyawasam “Mathematical Modeling and Dengue: An analysis of Incidence of Dengue in Urban Colombo using Wavelet Approach,” International Conference on Public Health Innovations, National Institute of Health Sciences, Sri Lanka, 2013, pp 49.
Sunmi Lee, and Carlos Castillo-Chavez “The role of residence time in two-patch dengue transmission dynamics and optimal strategies,” Journal of Theoretical Biology, vol. 374, 2015, pp 152-164.
Steven T. Stoddard, Amy C. Morrison, Gonzalo M. Vazquez-Prokopec, Valerie Paz Soldan, Tadeusz J. Kochel, Uriel Kitron, John P. Elder, and Thomas W. Scott, “The role of Human Movement in the transmission of Vector-Borne Pathogens,” PLOS Neglected Tropical Disease, vol. 3, No 7, 2009, pp e481
Sumith Pathirana, Mosato Kawabata, “Study of potential risk of dengue disease outbreak in Sri Lanka using GIS and statistical modeling,” Southern Cross University, vol 8, 2009, pp 8-17.