### A computational investigation on how visitation affects the reproduction number in a dengue fever model

#### Abstract

*R0.*Parameters for time spent in neighboring communities were varied in order to investigate how time spent in communities of different sizes affects the reproduction number. Results suggest that movement of individuals among communities increases the reproduction number, especially if people are traveling to a population of greater size.

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Aneke, S. (2002). Mathematical modelling of drug resistant malaria parasites and vector populations. Mathematical Methods in the Applied Sciences, 25(4):335–346.

Aron, J. L. and May, R. M. (1982). The population dynamics of malaria. In The population dynamics of infectious diseases: theory and applications, pages 139–179. Springer.

Auger, P., Kouokam, E., Sallet, G., Tchuente, M., and Tsanou, B. (2008). The Ross–Macdonald model in a patchy environment. Mathematical Biosciences, 216(2):123–131.

Browne, C., Huo, X., Magal, P., Seydi, M., Seydi, O., and Webb, G. (2014). A model of the 2014 ebola epidemic in West Africa with contact tracing. arXiv preprint arXiv:1410.3817.

CDC (2012). Symptoms and what to do if you think you have dengue. Centers for Disease Control and Prevention, http://www.cdc.gov/dengue/symptoms/. Accessed Aug. 2019.

Chowell, G., Diaz-Duenas, P., Miller, J., Alcazar-Velazco, A., Hyman, J., Fenimore, P., and Castillo-Chavez, C. (2007). Estimation of the reproduction number of dengue fever from spatial epidemic data. Mathematical Biosciences, 208(2):571–589.

Esteva, L. and Vargas, C. (1998). Analysis of a dengue disease transmission model. Mathematical Biosciences, 150(2):131–151.

Gubler, D. J. (1998). Resurgent vector-borne diseases as a global health problem. Emerging Infectious Diseases, 4(3):442.

Gubler, D. J. and Clark, G. G. (1995). Dengue/dengue hemorrhagic fever: the emergence of a global health problem. Emerging Infectious Diseases, 1(2):55.

Gubler, D. J., Ooi, E. E., Vasudevan, S., and Farrar, J. (2014). Dengue and dengue hemorrhagic fever. CABI.

Hughes, H. and Britton, N. F. (2013). Modelling the use of Wolbachia to control dengue fever transmission. Bulletin of Mathematical Biology, 75(5):796–818.

Kuniyoshi, M. L. G. and dos Santos, F. L. P. (2017). Mathematical modelling of vector-borne diseases and insecticide resistance evolution. Journal of Venomous Animals and Toxins including Tropical Diseases, 23(1):34.

Laughlin, C. A., Morens, D. M., Cassetti, M. C., Costero-Saint Denis, A., San Martin, J.-L., Whitehead, S. S., and Fauci, A. S. (2012). Dengue research opportunities in the Americas. Journal of Infectious Diseases, page jis351.

Lloyd, A. L., Zhang, J., and Root, A. M. (2007). Stochasticity and heterogeneity in host–vector models. Journal of The Royal Society Interface, 4(16):851–863.

Macdonald, G. (1957). The epidemiology and control of malaria. London, Oxford Univ. Pr.

MacDonald, G., Cuellar, C. B., and Foll, C. V. (1968). The dynamics of malaria. Bulletin of the World Health Organization, 38(5):743.

Maron, D. F. (2015). First dengue fever vaccine gets green light in 3 countries. https://www.scientificamerican.com/article/first-dengue-fever-vaccine-gets-green-lightin-3-countries/. Accessed Oct. 2016.

Martina, B. E., Koraka, P., and Osterhaus, A. D. (2009). Dengue virus pathogenesis: an integrated view. Clinical microbiology reviews, 22(4):564–581.

Monath, T. P. (1994). Dengue: the risk to developed and developing countries. Proceedings of the National Academy of Sciences, 91(7):2395–2400.

Osorio, L., Todd, J., and Bradley, D. J. (2004). Travel histories as risk factors in the analysis of urban malaria in Colombia. The American Journal of Tropical Medicine and Hygiene, 71(4):380–386.

Pinho, S. T. R. d., Ferreira, C. P., Esteva, L., Barreto, F., e Silva, V. M., and Teixeira, M. (2010). Modelling the dynamics of dengue real epidemics. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 368(1933):5679–5693.

Ranjit, S. and Kissoon, N. (2011). Dengue hemorrhagic fever and shock syndromes. Pediatric Critical Care Medicine, 12(1):90–100.

Reagan, K., Yokley, K. A., and Arangala, C. (2019). Simulations on a mathematical model of dengue fever with a focus on mobility. The North Carolina Journal of Mathematics and Statistics, 5:1–16. http://libjournal.uncg.edu/ncjms/article/view/1670.

Rodrıguez, D. J. and Torres-Sorando, L. (2001). Models of infectious diseases in spatially heterogeneous environments. Bulletin of Mathematical Biology, 63(3):547–571.

Sirisena, P. and Noordeen, F. (2014). Evolution of dengue in Sri Lanka—changes in the virus, vector, and climate. International Journal of Infectious Diseases, 19:6–12.

Soewono, E. and Supriatna, A. K. (2001). A two-dimensional model for the transmission of dengue fever disease. Bulletin of the Malaysian Mathematical Sciences Society, 24(1).

Time.is (2016). Peliyagoda on the map, http://time.is/Peliyagoda. Accessed Nov. 2016.

Torres-Sorando, L. and Rodrıguez, D. J. (1997). Models of spatio-temporal dynamics in malaria. Ecological Modelling, 104(2):231–240.

Van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1):29–48.

World Health Organization (2009). Dengue guidelines for diagnosis, treatment, prevention and control. World Health Organization.

worldatlas.com (2015a). Sri Lanka Facts, http://www.worldatlas.com/webimage/countrys/asia/srilanka/lkfacts.htm. Accessed Nov. 2016.

worldatlas.com (2015b). Where is sri jayewardenepura kotte, sri lanka?

http://www.worldatlas.com/as/lk/w/where-is-sri-jayewardenepura-kotte.html. Accessed Nov. 2016.

Yokley, K. A., Lee, J. T., Brown, A., Minor, M., and Mader, G. (2014). A simple agent-based model of malaria transmission investigating intervention methods and acquired immunity. Involve, a Journal of Mathematics, 7(1):15–40. https://msp.org/involve/2014/7-1/involve-v7-n1-p02-s.pdf.