Modified SIR for Vector-Borne Diseases Jacob Savos Katherine Kamis Colin Gay Benjamin Chua

Aims and Objectives To create a universal modified SIR model for vector-borne diseases to make predictions of the spread of diseases

Introduction A Vector-borne disease is transmitted by a pathogenic microorganism from an infected host to another organism HCI will be creating a model using Dengue Fever AOS will be creating a model using a tick- borne disease

Literature Review - Ticks Ticks have a two-year life cycle Ticks acquire a vector-borne disease by feeding on an infected host Once infected, ticks transmit the disease by feeding on an uninfected host Lone Star Tick Deer Tick

Literature Review – Dengue Fever A very old disease that reemerged in the past 20 years Transmitted via mosquito bites In 2009, there were a total of 4452 cases of dengue fever in Singapore, of which there were 8 deaths

Literature Review – Aedes Mosquitoes Aedes mosquitoes refers to the entire genus of mosquito – over 700 different species Multiple species able to transmit dengue fever Have characteristic black and white stripe markings on body and legs Aedes albopictus – the most invasive mosquito in the world Retrieved from edes-albopictus.jpg Aedes aegypti – Main vector of dengue fever in Singapore Retrieved from es/aedes-aegypti__ jpg

Literature Review - SIR Susceptible Infected Recovered

SIR - Equations S’(t) = -k * S(t) * I(t) I’(t) = -S’(t) – R’(t) R’(t) = c * I(t) ◦k – Transmittal constant ◦c – Recovery rate

Methodology Begin with a simple SIR model Develop variables needed to modify the model Attempt to modify the model to incorporate all vector-borne diseases

Timeline

Bibliography Academy of Science. Academy of Science Mathematics BC Calculus Text. Breish, N., & Thorne, B. (n.d.). Lyme disease and the deer tick in maryland. Maryland: The University of Maryland. Duane J. Gubler(1998, July). Clinical Microbiology Reviews, p , Vol. 11, No. 3, /98/$ Dengue and Dengue Hemorrhagic Fever. Retrieved November 3, 2010 from Neuwirth, E., & Arganbright, D. (2004). The active modeler: mathematical modeling with Microsoft Excel. Belmont, CA: Thomson/Brooks/Cole. Ministry of Health: FAQs. (n.d.). Dengue. Retrieved November 3, 2010, from KARR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJxLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZh ujU%2f343A5TwKDLTU0ml2TfH7cKB%2fJRT7PPvlAlopeq%2f%2be2n%2bmrW%2bZ%2fJts8OXGBj RP3hd0qhSL4 Ong, A., Sandar, M., Chen, M. l., & Sin, L. Y. (2007). Fatal dengue hemorrhagic fever in adults during a dengue epidemic in Singapore. International Journal of Infectious Diseases, 11, Stafford III, K. (2001). Ticks. New Haven: The Connecticut Agricultural Experiment Station.