Mathematical modeling of Echinococcus multilocularis transmission

Transcription

1 Biology Microbiology & Immunology ields Okayama University Year 2008 Mathematical modeling o Echinococcus multilocularis transmission Hiroumi Ishikawa Okayama University, ishikawa@ems.okayama-u.ac.jp This paper is posted at escholarship@oudir : Okayama University Digital Inormation Repository. and immunology/9

2 PI Supplement 44 by Ishikawa H with 20 Res and 3 Figs Mathematical modeling o Echinococcus multilocularis transmission Hiroumi Ishikawa* Department o Human Ecology, Graduate School o Environmental Science, Okayama University, Tsushimanaka, Okayama , Japan * Corresponding author. Tel: ; ax: address: ishikawa@ems.okayama-u.ac.jp (H. Ishikawa). 1

3 Abstract A mathematical model or the transmission cycle o Echinococcus multilocularis would be useul or estimating its prevalence, and the model simulation can be instrumental in designing various control strategies. This review ocuses on the epidemiological actors in the E. multilocularis transmission cycle and the recent advances o mathematical models or E. multilocularis transmission. Keywords: Echinococcus multilocularis; Fox; Mathematical model; Vole. 2

4 1. Introduction Echinococcus multilocularis is distributed in central Europe, North America, and northern and central Eurasia [1]. In Japan, human alveolar Echinococcus (HAE) caused by E. multilocularis has spread throughout the mainland o Hokkaido [2], making it desirable to design eective control strategies against HAE. It is diicult to elucidate the source o inections due to the long incubation period [3]. A mathematical model or the transmission cycle o E. multilocularis would be useul or estimating its prevalence, and the model simulation can be instrumental in designing various control strategies. A ew models about E. multilocularis transmission have been proposed since 1995 [4-6]. This review ocuses on the epidemiological actors in the E. multilocularis transmission cycle and the recent advances o mathematical models or E. multilocularis transmission. E. multilocularis carries out its transmission cycle in two hosts; the deinitive hosts are canines, while the intermediate hosts are mainly rodents and ungulates [1, 7-9]. Individuals are inected by the accidental ingestion o parasite eggs. The intermediate hosts are inected by ingesting parasite eggs voided in the eces o inected deinitive hosts, while the deinitive hosts are inected by preying on the intermediate hosts that have hydatid cysts. A mathematical model which quantitatively describes the 3

5 transmission o E. multilocularis needs to include the ollowing components [5, 10] 1. dynamics o deinitive host population 2. dynamics o intermediate host population 3. predator-prey relationship between the deinitive hosts (canines) and the intermediate hosts (rodents) 4. longevity o parasite eggs in the environment. 2. Dynamics o deinitive hosts Foxes mainly maintain the transmission cycle o E. multilocularis. The major deinitive host is the red ox (Vulpes vulpes) or most endemic regions, or the arctic ox (Alopex lagopus) or the tundra zone o Eurasia and North America [1, 7, 9, 11]. The dynamics o the ox population show marked seasonal variations because oxes are wild animals. Thereore, a quantitative transmission model needs to include a host population dynamic component [5]. In Hokkaido, Japan, the breeding season o red oxes is generally early spring (the last third o March - the irst third o April) and newborns ater weaning, which might be exposed to E. multilocularis inection, emerge rom their dens one month ater birth [12]. Generally, or any wild animal the death rate o juveniles is signiicantly higher than that o adults. The death rate o juvenile (under 1 4

6 year old) red oxes in Hokkaido was estimated to be 2.5 times higher than that o adults [5]. The seasonal population model o red ox density in Hokkaido is shown in Fig. 1. The arctic ox population is also inluenced by emigration and immigration due to long-distance traveling [11]. 3. Dynamics o intermediate hosts Rodents mainly maintain the transmission cycle o E. multilocularis as the intermediate hosts, and the species that are involved in the cycle vary in dierent endemic regions [1, 9]. In Hokkaido, the major intermediate host is the gray-sided vole (Clethrionomys ruocanus) [7]. The gray-sided vole breeds in three seasons o the year (all seasons except winter) [13, 14]. The survival rate o voles depends on the season and age, with that or the irst month o lie being lower than that o >1 month [13, 14], while the survival rate in winter is higher than that in summer [15]. Besides the season variation, the dynamics o the vole population vary on a large scale annually, and have certain geographical characteristics [16]. There is no necessity to consider emigration or immigration in the dynamics o the vole population because o the small size o home ranges [13]. 5

7 4. Transmission processes o Echinococcus multilocularis The deinitive host is inected with E. multilocularis by preying on rodents which harbor multilocular Echinococcus with inectious protoscoleces. Thereore, the prevalence o E. multilocularis is aected by the average number (NVF) o voles ingested by a ox each day, which depends on the density o the vole population and on the depth o the snow actors [17, 18], which were introduced into the transmission model [5]. The intermediate host is inected by ingesting E. multilocularis eggs voided in the eces o inected deinitive hosts. The duration o the egg s inectious ability is mainly aected by temperature and humidity. The tenacity o eggs is sensitive to elevated temperature, to very low temperature and to desiccation [19]. The experimental ormula or the longevity (d days) o eggs at temperature (t o C) was established as d = exp[-0.135(t-43.7)] [20]. 5. Mathematical models o Echinococcus multilocularis transmission A deterministic model or the transmission o a parasite essentially describes its transmission cycle as a set o dierential equations. Roberts and Aubert [4] constructed a simple deterministic E. multilocularis transmission model to evaluate the eect o 6

8 control by addition o praziquantel in France. Ishikawa et al. [5] proposed a model that took into account the inluence o the dynamics o both the deinitive and the intermediate host populations and the seasonal eects on the longevity o E. multilocularis eggs and NVF to describe the mechanism o seasonal transmission in Hokkaido quantitatively. Hansen et al. [6] tried to develop a stochastic transmission model rom the Roberts and Aubert model to devise a hypothesis that would it well with the prevalence data during the pre- and post-control periods in the northern Germany. In these models [4-6], each host population is broadly divided into three epidemiology classes. Moreover, in the quantitative model shown in Fig.2 [5], the inected egg-producing class in oxes is subdivided into two subclasses according to whether egg production is abundant or not. The basic reproductive rate (R 0 ) is the theoretically maximum number o secondary inections. R 0 was estimated rom the Roberts and Aubert model [4] or the model o Ishikawa et al. excluding seasonal actors [5] as ollows: R 0 = δ v t ( 1+ δ τ )( 1+ δ τ )( 1+ δ η ) v v λ λ N v t η R 0 = δ v s NVFλ N v ρη + ( )( )( ) h 1+ δ vτ v 1+ δ τ 1+ δ η h 1+ δ ηl η l 7

9 The symbols λ a, δ a, τ a, s, NVF, N, η t η h, l, η, and ρ represent the inectious contact rate (a=s, v), the death rate (a=s, v), the period o no egg production (a=) or or acquiring inectious protoscoleces (a=v) expressed as days ater inection, the conditional probability o maturity o worms (), the average NVF, the average o density (), the durations o total, high and low egg production, and the multiplicative actor caused by high egg production, with the suixes and v standing or ox and vole, respectively. The seasonal variations o the prevalence and the density o inected oxes were simulated or the two endemic regions in Hokkaido, Japan: Nemuro and Abashiri, where the average prevalence rates ( ) were 53% and 48%, respectively. There is a great dierence between the two regions in terms o snowall. Comparison o two regions using the model simulation shows that the winter density o the inected oxes is maintained at a certain level in Nemuro, while it alls to a low level in Abashiri, which leads to the dierence o the winter prevalence between Nemuro and Abashiri (Fig. 3) [5]. 6. Risk o HAE 8

10 The risk to the human population o being inected with HAE has a close relation to the amount o E. multilocularis eggs that maintain inectious ability in the environment. A comparative study on the risk o HAE between Sapporo, the capital o Hokkaido, and Nemuro was carried out by simulating the seasonal luctuation in E. multilocularis egg dispersion in the environment based on the model [5]. 7. Prospects Recent advances in mathematical modeling o E. multilocularis transmission were summarized here. There has been steady progress in mathematical modeling o E. multilocularis transmission into consideration taking seasonal actors. Further ollow-up studies based on ield data will be needed to precisely estimate the eects o control strategies against E. multilocularis using model simulations. Acknowledgements This work was supported in part by a Grant-in-Aid or Scientiic Research rom the Japan Society or the Promotion o Science (Grant No ) and by grants rom the Ministry o Health, Labour and Welare, Japan or The control o emerging and reemerging diseases in Japan (Principal investigator: Pro. M. Kamiya). 9

11 Reerences [1] Eckert J, Gemmell MA, Meslin FX, Pawlowski ZS. WHO/OIE Manual on Echinococcosis in Human and Animals: a Public Health Problem o Global Concern. Paris: World Organisation or Animal Health, [2] Annual Reports o the Council or Alveolar Echinococcus in Hokkaido Department o Health and Welare, Hokkaido Government, Sapporo, [3] Doi R, Nakao M, Nihei N, Kutsumi H. Epidemiology o alveolar hydatid disease (AHD) and estimation o inected period o AHD in Rebun Island, Hokkaido. Jpn J Public Health 2000; 47: (in Japanese with English abstract). [4] Roberts MG, Aubert MFA. A model or the control o Echinococcus multilocularis in France. Vet Parasitol 1995; 56: [5] Ishikawa H, Ohga Y, Doi R. A model or the transmission o Echinococcus multilocularis in Hokkaido, Japan. Parasitol Res 2003; 91: [6] Hansen F, Tackmann K, Jeltsch F, Wissel C, Thulke H-H. Controlling Echinococcus multilocularis- ecological implications o ield trails. Prev Vet Med 2003; 60: [7] Ohbayashi M. Host animals o Echinococcus multilocularis in Hokkaido. In: Uchino J, Sato N, editors. Alveolar Echinococcosis: strategy or eradication o alveolar 10

12 echinococcosis o the liver. Sapporo: Fujishoin, 1996; [8] Petavy AF, Deblock S, Walbaum S. Lie cycles o Echinococcus multilocularis in relation to human inection. J Parasitol 1991; 77: [9] Rausch RL. Lie cycle patterns and geographic distribution o Echinococcus species. In: Thompson RCA, Lymbery AJ eds. Echinococcus and hydatid diseases. Wallingord Oxon: CAB International, 1995; [10] Saitoh T, Takahashi K. The role o vole populations in prevalence o the parasite (Echinococcus multilocularis) in oxes. Res Popul Ecol. 1998; 40: [11] Fay FH, Rausch RL. Dynamics o the arctic ox population on St. Lawrence Island, Bering Sea. Arctic 1992; 45: [12] Uraguchi K, Takahashi K. Ecology o the red ox in Hokkaido. In: Tsuduki T, editor. Alveolar Echinococcus in Hokkaido. Sapporo: Hokkaido Institute o Public Health, 1999; (in Japanese). [13] Ota K. Study on wild murid rodents in Hokkaido. Sapporo: Hokkaido University Press, 1984 (in Japanese). [14] Yoccoz NG, Nakata K, Stenseth NC, Saitoh T. The demography o Clethrionomys ruocanus: rom mathematical and statistical models to urther ield studies. Res Popul Ecol 1998; 40:

13 [15] Dewa H. Seasonal variation o the daily activity rhythms in snow season. Res Bull College Exp Forests Hokkaido Univ 1975; 22: (in Japanese with English summery). [16] Saitoh T, Stenseth NC, Bjornstad ON. The population dynamics o the vole Clethrionomys ruocanus in Hokkaido, Japan. Res Popul Ecol 1998; 40: [17] Abe H. Winter Food o red ox, Vulpes vulpes schrencki Kishida, in Hokkaido, with Special reerence to vole populations. Appl Ent Zool 1975; 10: [18] Yoneda, M. Inluence o red ox predation upon a local population o small rodents Ⅲ. Seasonal changes in predation pressure, prey preerence and predation eect. Appl Ent Zool 1983; 18: [19] Veit P, Bilger B, Schad V, Schaer J, Frank W, Lucius R. Inluence o environmental actors on the inectivity o Echinococcus multilocularis eggs. Parasitology. 1995; 110: [20] Ishige M, Itoh T and Yagi K. Biological characters o Echinococcus multilocularis on temperature eects on lie span o eggs. Rep Hokkaido Inst Public Health 1993; 43: (in Japanese with English summary). 12

14 Legends Fig. 1 The seasonal population dynamics models or oxes and voles in Hokkaido. The solid line and the dotted line shows the variations in ox and vole density /km 2, respectively [5] Fig. 2 The basic scheme or the model o the Echinococcus multilocularis transmission cycle between oxes (the major deinitive host) and voles (the major intermediate host). Fig. 3 Seasonal variations in the density/km 2 o oxes inected with E. multilocularis (solid line) and the prevalence o E. multilocularis in the ox population (broken line). The black and gray lines show the Nemuro and Abashiri situations, respectively [5]. 13