Mathematical modeling of Leptospirosis spread in Malaysia

Leptospirosis is a zoonotic disease that is caused by the pathogen Leptospira, and it can spread indirectly or directly from infected animals to humans.  According to the official statistics from the Malaysian Ministry of Health, leptospirosis outbreaks appeared to be in the most critical condition in the recent few years.  The Susceptible--Infected--Recovered compartmental model and its extensions have been applied widely in disease modeling.  This paper aims to present a compartmental model for leptospirosis spread in Malaysia.  Using this approach, an epidemiological model is formulated for humans and vector populations.  Our results indicate that the transmission rate from susceptible to infected vectors and the vector birth rate play a significant role in determining the number of infected humans.  Besides, they have an impact on the duration of the outbreak as well.  The simulation results have been compared with the actual data in 2017 and the analysis shows that the proposed model is able to predict the outbreak recorded in Malaysia.

Leptospirosis
transmission
математичне моделювання
SIR model
  1. Levett P. N.  Leptospirosis.  Clinical Microbiology Reviews. 14 (2), 296 (2001).
  2. Gupta V., Bala N.  Leptospirosis: A Disease of Public Health Importance.  International Journal of Medical Sciences. 9 (1), 43–49 (2016).
  3. Stimson A. M.  Note on an organism found in yellow-fever tissue.  Public Health Reports (1896–1907). 22 (18), 541 (1907).
  4. Inada R., Ido Y.  A Report on the Discovery of the Causal Organism (a New Species of Spirochaeta) of Weil's Disease.  Tokyo Ijishinshi. 1908, 351 (1915).
  5. Kumbhare M. R., Surana A. R., Arote R. A., Borse G. D.  Current Status of Leptospirosis: A Zoonotic Tropical Disease.  International Journal of Microbiology and Current Research. 1 (1), 14–19 (2019).
  6. Noguchi H.  The Spirochaetes.  In E. O. Jordan, I. S. Falk (Eds.), The Newer Knowledge of Bacteriology and Immunology.  University of Chicago Press (1928).
  7. World Health Organisation.  Human Leptospirosis: Guidance for Diagnosis, Surveillance and Control. http://apps.who.int/iris/bitstream/10665/42667/1/WHO_CDS_CSR_EPH_2002.23.pdf (2003).
  8. Thibeaux R., Geroult S., Benezech C., Chabaud S., Soupe-Gilbert M.-E., Girault D., Bierque E., Goarant C.  Seeking the environmental source of Leptospirosis reveals durable bacterial viability in river soils.  PLOS Neglected Tropical Diseases. 11 (2), e0005414 (2017).
  9. Pappas G., Papadimitriou P., Siozopoulou V., Christou L., Akritidis N.  The globalization of leptospirosis: worldwide incidence trends.  International Journal of Infectious Diseases. 12 (4), 351–357 (2008).
  10. Garba B., Bahaman A. R., Khairani-Bejo S., Zakaria Z.,  Mutalib A. R.  Retrospective Study of Leptospirosis in Malaysia.  EcoHealth. 14, 389–398 (2017).
  11. Lee L. T.  Declare all-out war on rats.  The Star Malaysia (2017).
  12. Bharti A. R., Nally J. E., Ricaldi J. N., Matthias M. A., Diaz M. M., Lovett M. A., Levett P. N., Gilman R. H., Willig M. R., Gotuzzo E., Vinetz J. M.  Leptospirosis: a zoonotic disease of global importance.  The Lancet Infectious Disease. 3 (12), 757–771 (2003).
  13. Pongsumpun P.  Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans.  International Journal of Mathematical and Computational Sciences. 6 (12), 1639–1644 (2012).
  14. Triampo W., Baowan D., Tang I. M., Nuttavut N., Wong-Ekkabut J., Doungchawee G.  A Simple Deterministic Model for the Spread of Leptospirosis in Thailand.  International Journal of Biomedical Sciences. 2 (1), 22–26 (2007).
  15. Khan M. A., Islam S., Khan S. A., Khan I., Shafie S., Gul T.  Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables.  Abstract and Applied Analysis. 2014, Article ID 619035 (2014).
  16. Department of Statistics Malaysia.  Current Population Estimates, Malaysia, 2017–2018 (2018). https://www.dosm.gov.my/v1/index.php?r=column/cthemeByCat&cat=155&bul_id=c1pqTnFjb29HSnNYNUpiTmNWZHArdz09&menu_id=L0pheU43NWJwRWVSZklWdzQ4TlhUUT09.
  17. Department of Statistics Malaysia.  Vital Statistics, Malaysia, 2017–2018 (2018). https://www.dosm.gov.my/v1/index.php?r=column/cthemeByCat&cat=165&bul_id=Z1VxWjBnQXRFblE0ZDVKbFJSSFFZdz09&menu_id=L0pheU43NWJwRWVSZklWdzQ4TlhUUT09#.
  18. Department of Statistics Malaysia.  Abridged Life Tables, Malaysia, 2016–2018 (2018). https://www.dosm.gov.my/v1/index.php?r=column/cthemeByCat&cat=116&bul_id=aDV6TWxoU0NlNVBYN1hXM1Y0L2Jadz09&menu_id=L0pheU43NWJwRWVSZklWdzQ4TlhUUT09.
  19. Izurieta R., Galwankar S., Clem A.  Leptospirosis: The "mysterious" mimic.  Journal of Emergencies, Trauma, and Shock. 1 (1), 21–23 (2008).
  20. Leptospirosis Information Center.  Overview of human leptospirosis – guide for the public.  http://www.leptospirosis.org/human-leptospirosis-guide/.
  21. Andreollo N. A., Santos E. F., Araujo M. R., Lopes L. R.  Rat's Age Versus Human's Age: What is the Relationship?  ABCD Arquivos Brasileiros de Cirurgia Digestiva. 25 (1), 49–51 (2012).
  22. Benacer D., Thong K. L., Verasahib K. B., Galloway R L., Hartskeerl R. A., Lewis J. W.,  Zain S. N. M.  Human Leptospirosis in Malaysia: Reviewing the Challenges After 8 Decades (1925–2012).  Asia Pacific Journal of Public Health. 28 (4), 290–302 (2016).