Modeling of transmission pathways on canine heartworm dynamics

  • Seo, Sat Byul (Department of Mathematics Education, Kyungnam University)
  • Received : 2019.10.11
  • Accepted : 2019.12.16
  • Published : 2020.03.31


Canine heartworm disease is a vector-borne disease that is transmitted from dog to dog by mosquitoes. It causes epidemics that disrupt the health environments of dogs and are burdensome for many dog owners. Recent trends of changing temperatures and weather conditions in South Korea may have an impact on the population of mosquitoes, and it affects the population of dogs at risk of heartworm infection. Mathematical modeling has become an important measure for analyzing the epidemiological characteristics of infectious diseases. However, canine heartworm infection transmission has not been reported yet through mathematical modeling. We develop a mathematical model of canine heartworm infection to predict the population of infected dogs depending on the vector (mosquito) population using a susceptible, exposed, infected, and recovered model. Simulation results show that after 1 year, 3,289 dogs out of 73,602 (about 4.5%) are exposed and 134 (about 0.2%) are infected. Only 0.2% of susceptible dogs become infected after 1 year. However, if all exposed dogs are maintained in the same circumstances without any treatment, then the number of infected subjects will increase over time. This may increase the possibility of other dogs, especially dogs that live outside, being infected.


  1. American Heartworm Society. FAQs. American Heartworm Society, Wilmington, 2014. Available from:
  2. Bowman DD, Liu Y, McMahan CS, Nordone SK, Yabsley MJ, Lund RB. Forecasting United States heartworm Dirofilaria immitis prevalence in dogs. Parasit Vectors 2016;9:540.
  3. Hwang WK, Chung GS, Kim DY. Pet Reports 2018: Pet Related Industries and Parenting Status. KB Financial Group Inc., Seoul, 2018.
  4. Campbell-Lendrum D, Manga L, Bagayoko M, Sommerfeld J. Climate change and vector-borne diseases: what are the implications for public health research and policy? Philos Trans R Soc Lond B Biol Sci 2015;370:370.
  5. Kim JW, Bu KO, Choi JT, Byun YH. Climate Change in the Korean Peninsula for 100 Years. National Institute of Meteorological Sciences, Jeju, 2018.
  6. van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 2002;180:29-48.
  7. Coyne MJ, Smith G, McAllister FE. Mathematic model for the population biology of rabies in raccoons in the mid-Atlantic states. Am J Vet Res 1989;50:2148-2154.
  8. Manore CA, Hickmann KS, Xu S, Wearing HJ, Hyman JM. Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus. J Theor Biol 2014;356:174-191.
  9. Olawoyin O, Kribs C. Effects of multiple transmission pathways on Zika dynamics. Infect Dis Model 2018;3:331-344.
  10. American Veterinary Medical Association. Heartworm Disease. American Veterinary Medical Association, Schaumburg. Available from:
  11. Ji IB, Kim HJ, Kim WT, Seo GC. Development Strategies for the Companion Animal Industry. Korea Rural Economic Institute, Naju, 2017. Available from:
  12. Shutt DP, Manore CA, Pankavich S, Porter AT, Del Valle SY. Estimating the reproductive number, total outbreak size, and reporting rates for Zika epidemics in South and Central America. Epidemics 2017;21:63-79.
  13. Yang HM, Macoris ML, Galvani KC, Andrighetti MT, Wanderley DM. Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue. Epidemiol Infect 2009;137:1188-1202.
  14. Asamoah JK, Oduro FT, Bonyah E, Seidu B. Modeling of rabies transmission dynamics using optimal control analysis. J Appl Math 2017;2017:2451237.
  15. Zhang J, Jin Z, Sun GQ, Zhou T, Ruan S. Analysis of rabies in China: transmission dynamics and control. PLoS One 2011;6:e20891.