A mathematical model for assessing the effectiveness of controlling relapse in Plasmodium vivax malaria endemic in the Republic of Korea


Autoři: Sungchan Kim aff001;  Jong Hyuk Byun aff001;  Anna Park aff001;  Il Hyo Jung aff001
Působiště autorů: Department of Mathematics, Pusan National University, Geumjeong-Gu, Busan 46241, Republic of Korea aff001;  Finance · Fishery · Manufacture Industrial Mathematics Center on Big Data, Pusan National University, Geumjeong-Gu, Busan 46241, Republic of Korea aff002
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0227919

Souhrn

Malaria has persisted as an endemic near the Demilitarized Zone in the Republic of Korea since the re-emergence of Plasmodium vivax malaria in 1993. The number of patients affected by malaria has increased recently despite many controls tools, one of the reasons behind which is the relapse of malaria via liver hypnozoites. Tafenoquine, a new drug approved by the United States Food and Drug Administration in 2018, is expected to reduce the rate of relapse of malaria hypnozoites and thereby decrease the prevalence of malaria among the population. In this work, we have developed a new transmission model for Plasmodium vivax that takes into account a more realistic intrinsic distribution from existing literature to quantify the current values of relapse parameters and to evaluate the effectiveness of the anti-relapse therapy. The model is especially suitable for estimating parameters near the Demilitarized Zone in Korea, in which the disease follows a distinguishable seasonality. Results were shown that radical cure could significantly reduce the prevalence level of malaria. However, eradication would still take a long time (over 10 years) even if the high-level treatment were to persist. In addition, considering that the vector’s behavior is manipulated by the malaria parasite, relapse repression through vector control at the current level may result in a negative effect in containing the disease. We conclude that the use of effective drugs should be considered together with the increased level of the vector control to reduce malaria prevalence.

Klíčová slova:

Infectious disease control – Korea – Malaria – Malarial parasites – Mosquitoes – Parasitic diseases – Plasmodium – South Korea


Zdroje

1. Feighner BH, Pak SI, Novakoski WL, Kelsey LL, Strickman D. Reemergence of Plasmodium vivax malaria in the republic of Korea. Emerging Infectious Diseases. 1998;4(2):295. 9621202

2. Naing C, Whittaker MA, Wai VN, Mak JW. Is Plasmodium vivax malaria a severe malaria?: a systematic review and meta-analysis. PLoS Neglected Tropical Diseases. 2014;8(8):e3071. doi: 10.1371/journal.pntd.0003071 25121491

3. Im JH, Kwon HY, Baek J, Park SW, Durey A, Lee KH, et al. Severe Plasmodium vivax infection in Korea. Malaria Journal. 2017;16(1):51. doi: 10.1186/s12936-017-1684-4 28129766

4. Markus MB. Malaria: origin of the term “hypnozoite”. Journal of the History of Biology. 2011;44(4):781–786. doi: 10.1007/s10739-010-9239-3 20665090

5. Lover AA, Zhao X, Gao Z, Coker RJ, Cook AR. The distribution of incubation and relapse times in experimental human infections with the malaria parasite Plasmodium vivax. BMC Infectious Diseases. 2014;14(1):539. doi: 10.1186/1471-2334-14-539 25280926

6. Cappellini MD, Fiorelli G. Glucose-6-phosphate dehydrogenase deficiency. The Lancet. 2008;371(9606):64–74. doi: 10.1016/S0140-6736(08)60073-2

7. 2019 malaria control manual. Korea Centers for Disease Control and Prevention (KCDC); 2019. Available from: http://www.cdc.go.kr/CDC/cms/content/mobile/06/143706_view.html.

8. Yeom JS, Park YK. Treatment of Korean vivax malaria in Korea. Journal of the Korean Medical Association. 2007;50(1):88–92. doi: 10.5124/jkma.2007.50.1.88

9. Lacerda MV, Llanos-Cuentas A, Krudsood S, Lon C, Saunders DL, Mohammed R, et al. Single-dose tafenoquine to prevent relapse of Plasmodium vivax malaria. New England Journal of Medicine. 2019;380(3):215–228. doi: 10.1056/NEJMoa1710775 30650322

10. Llanos-Cuentas A, Lacerda MV, Hien TT, Vélez ID, Namaik-larp C, Chu CS, et al. Tafenoquine versus primaquine to prevent relapse of Plasmodium vivax malaria. New England Journal of Medicine. 2019;380(3):229–241. doi: 10.1056/NEJMoa1802537 30650326

11. Roy M, Bouma MJ, Ionides EL, Dhiman RC, Pascual M. The potential elimination of Plasmodium vivax malaria by relapse treatment: insights from a transmission model and surveillance data from NW India. PLoS Neglected Tropical Diseases. 2013;7(1):e1979. doi: 10.1371/journal.pntd.0001979 23326611

12. Lloyd AL. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theoretical Population Biology. 2001;60(1):59–71. doi: 10.1006/tpbi.2001.1525 11589638

13. Wearing HJ, Rohani P, Keeling MJ. Appropriate models for the management of infectious diseases. PLoS Medicine. 2005;2(7):e174. doi: 10.1371/journal.pmed.0020174 16013892

14. Brooks-Pollock E, Cohen T, Murray M. The impact of realistic age structure in simple models of tuberculosis transmission. PLoS One. 2010;5(1):e8479. doi: 10.1371/journal.pone.0008479 20062531

15. Vergu E, Busson H, Ezanno P. Impact of the infection period distribution on the epidemic spread in a metapopulation model. PLoS One. 2010;5(2):e9371. doi: 10.1371/journal.pone.0009371 20195473

16. Krylova O, Earn DJ. Effects of the infectious period distribution on predicted transitions in childhood disease dynamics. Journal of The Royal Society Interface. 2013;10(84):20130098. doi: 10.1098/rsif.2013.0098

17. Nah K, Kim Y, Lee JM. The dilution effect of the domestic animal population on the transmission of P. vivax malaria. Journal of Theoretical Biology. 2010;266(2):299–306. doi: 10.1016/j.jtbi.2010.06.032 20619273

18. Nah K, Nakata Y, Röst G. Malaria dynamics with long incubation period in hosts. Computers & Mathematics with Applications. 2014;68(9):915–930. doi: 10.1016/j.camwa.2014.05.001

19. Kim JE, Choi Y, Lee CH. Effects of climate change on Plasmodium vivax malaria transmission dynamics: A mathematical modeling approach. Applied Mathematics and Computation. 2019;347:616–630. doi: 10.1016/j.amc.2018.11.001

20. Kim SJ, Kim SH, Jo SN, Gwack J, Youn SK, Jang JY. The long and short incubation periods of Plasmodium vivax malaria in Korea: the characteristics and relating factors. Infection & Chemotherapy. 2013;45(2):184–193. doi: 10.3947/ic.2013.45.2.184

21. Battle KE, Karhunen MS, Bhatt S, Gething PW, Howes RE, Golding N, et al. Geographical variation in Plasmodium vivax relapse. Malaria Journal. 2014;13(1):144. doi: 10.1186/1475-2875-13-144 24731298

22. Chu CS, White NJ. Management of relapsing Plasmodium vivax malaria. Expert Review of Anti-Infective Therapy. 2016;14(10):885–900. doi: 10.1080/14787210.2016.1220304 27530139

23. Yeom JS, Park JW. Status of vivax malaria after re-emergence in South Korea. Infection and Chemotherapy. 2008;40(4):191–198. doi: 10.3947/ic.2008.40.4.191

24. Warrell DA, Gilles HM. Essential malariology. CRC Press; 2017.

25. Koole G. A formula for tail probabilities of Cox distributions. Journal of Applied Probability. 2004;41(3):935–938. doi: 10.1239/jap/1091543436

26. Buchholz P, Kriege J, Felko I. Input modeling with phase-type distributions and Markov models: theory and applications. Springer; 2014.

27. Diekmann O, Heesterbeek JAP, Metz JA. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology. 1990;28(4):365–382. doi: 10.1007/bf00178324 2117040

28. Inaba H. On a new perspective of the basic reproduction number in heterogeneous environments. Journal of Mathematical Biology. 2012;65(2):309–348. doi: 10.1007/s00285-011-0463-z 21842424

29. Bacaër N, Guernaoui S. The epidemic threshold of vector-borne diseases with seasonality. Journal of Mathematical Biology. 2006;53(3):421–436. doi: 10.1007/s00285-006-0015-0 16823580

30. Inaba H. The basic reproduction number R0 in time-heterogeneous environments. Journal of Mathematical Biology. 2019; p. 1–34.

31. Kim S, Byun JH, Jung IH. Global stability of an SEIR epidemic model where empirical distribution of incubation period is approximated by Coxian distribution. Advances in Difference Equations. 2019;2019(1):469. doi: 10.1186/s13662-019-2405-9

32. Kakizoe Y, Nakaoka S, Beauchemin CA, Morita S, Mori H, Igarashi T, et al. A method to determine the duration of the eclipse phase for in vitro infection with a highly pathogenic SHIV strain. Scientific reports. 2015;5:10371. doi: 10.1038/srep10371 25996439

33. Akaike H. Information theory and an extension of the maximum likelihood principle. In: Selected papers of hirotugu akaike. Springer; 1998. p. 199–213.

34. Massad E, Coutinho FAB, Lopez LF, Da Silva DR. Modeling the impact of global warming on vector-borne infections. Physics of Life Reviews. 2011;8(2):169–199. doi: 10.1016/j.plrev.2011.01.001 21257353

35. Gao D, Lou Y, He D, Porco TC, Kuang Y, Chowell G, et al. Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis. Scientific Reports. 2016;6:28070. doi: 10.1038/srep28070 27312324

36. Ishikawa H, Ishii A, Nagai N, Ohmae H, Harada M, Suguri S, et al. A mathematical model for the transmission of Plasmodium vivax malaria. Parasitology International. 2003;52(1):81–93. doi: 10.1016/s1383-5769(02)00084-3 12543150

37. Garrett-Jones C. The human blood index of malaria vectors in relation to epidemiological assessment. Bulletin of the World Health Organization. 1964;30(2):241. 14153413

38. Feng X, Zhang S, Huang F, Zhang L, Feng J, Xia Z, et al. Biology, bionomics and molecular biology of Anopheles sinensis Wiedemann 1828 (Diptera: Culicidae), main malaria vector in China. Frontiers in Microbiology. 2017;8:1473. doi: 10.3389/fmicb.2017.01473 28848504

39. Agency CI. The world factbook. Available from: http://www.cia.gov/library/publications/the-world-factbook/.

40. Cator LJ, Lynch PA, Read AF, Thomas MB. Do malaria parasites manipulate mosquitoes? Trends in Parasitology. 2012;28(11):466–470. doi: 10.1016/j.pt.2012.08.004 23044288

41. Cator LJ, Lynch PA, Thomas MB, Read AF. Alterations in mosquito behaviour by malaria parasites: potential impact on force of infection. Malaria Journal. 2014;13(1):164. doi: 10.1186/1475-2875-13-164 24885783

42. Churcher TS, Trape JF, Cohuet A. Human-to-mosquito transmission efficiency increases as malaria is controlled. Nature Communications. 2015;6:6054. doi: 10.1038/ncomms7054 25597498

43. Spence Beaulieu MR. The role of parasite manipulation in vector-borne diseases. Evolution, medicine, and public health. 2019;2019(1):106–107. doi: 10.1093/emph/eoz019 31289686


Článek vyšel v časopise

PLOS One


2020 Číslo 1