Kendali Optimal Model Siklus Hidup Cacing Schistosoma japonicum dengan Prinsip Minimum Pontryagin

Sriwahyuni Sriwahyuni, Rina Ratianingsih, Hajar Hajar

Abstract


Schistosomiasis is an infectious disease caused by trematodes, of the genus Schistosoma. In Indonesia the disease is caused by Schistosoma japonicum. The worm life cycle is specific because its habitat is not only on human body or some other mammal but also in snail. This research is aimed to a mathematical model of the worm cycle and investigates the optimal control of the model. The mathematically control was conducted by put a time dependent parameter ρ (t) to the model that represents a medical treatment to infected humans. The governed model, that has an endemic stable critical point, describes a transferred worm cycle of several phases. The optimal control is determined by the Minimum Pontryagin Principle. The simulation of the model shows that, for such initial condition of the uncontrolled model, the number of adult worms will increase up to 4700 in 80 days. This number could reduce to 4500 on the day of 100 and converge to 4400for unbounded time growth. It means that schistosomiasis is permanently occurring (endemic). The controlled model gives as the drug dose of praziquantel. The drug doze of 20 mg praziquantel could minimize the growth of worms and decreasethe number of adult worm population to 8 in 6 months.

Keywords


optimal control; Pontryagin minimum principle; Schistosoma japonicum

References


Barrington, e.r .s., a.j. willis, and M. A. Sleich. A

Series of Student T exts in Contemporary

Biology . Edward Arnold Limited, London. 1979.

Andrew D. Schistosomiasis. In: Gordon C. Cook,

Alimuddin L Z, editors. Manson's Tropical

Diseases. 21 ed. China: Saunders Elsevier:

;82:1425

Miyazaki, I. An Illustrated Book of Helminthic

Zoonosis. International Medical Foundation of

Japan, T okyo. 1991.

Fischer PR, Summer AP , White CA, Jr . In: Ralph

D. Feigin, James DC, Gail JDH, Sheldon L Kaplan,

editors. Textbook of Pediatric Infectious

Diseases. 6 ed. United States of America:

Saunders Elsevier: 2009;240:3023.

Safar R. Parasitologi Kedokteran. Protozoologi,

Helmintologi, Entomologi. 1 st ed. Bandung:

CV . Y rama Widya; 2009.h: 208.

Zhou XN, Bergquist R, Leonardo L, Olveda R.

Schistosomiasis: The Disease and its Control.

September . Accessed September 18,

0 1 3 . A v a i l a b l e f r o m :

http://www.rnas.org.cn/upload/inFile/2008

-9-25160310-Schistosomiasis.pdf

Weekly epidemiological record 30 April No. 18,

0 1 0 , 8 5 , 1 5 7 - 1 6 4 . Wo r l d H e a l t h

Organization. Accessed September 18, 2013.

Available from: http://www .who.int/wer .

Chistulo L, Loverde P , Engels D. Disease Watch:

S c h i s t o s o mi a s i s . T D R N a t u r e Re v i e ws

Microbiology. 2004; 2:12

Steinmann P . Epidemiology and Diagnosis of

Schi s t os oma j aponi c um ot her hel mi nt h

infections and multiparasitism in Yunan

p r ov i n c e , Pe o p l e' s Re p u b l i c o f C h i n a .

(dissertation). (German): University of Basel;

Hadidjaja, P . Beberapa penelitian mengenai

aspek biologik dan klinik schistosomiasis di

Sulawesi T engah, Indonesia. Thesis Doktor

Universitas Indonesia. 1982. 2013;3(3):31–42.

Jastal, Gardjito T A, Anastasia H, Mujiyanto.

A n a l i s i s S p a s i a l e p i d e m i o l o g i

schistosomiasis menggunakan pengindraan

jauh dan system informasi geografis di

Lembah Napu dan Lindu Kab.

Sudomo M. Penyakit Parasitik Y ang Kurang

Diperhatikan di Indonesia.Jakarta : Badan

Penelitian dan Pengembangan Kesehatan

Departemen Kesehatan Republik Indonesia.

Davis, G.M., and W.P . carney .. Descriptionof

On c o me l a n i a h u p e n s i s l i n d o e n s i s : f i r s t

intermediate host of Schistosoma japonicum in

Sulawesi. Proc. Acad. Nat. Sci. Philadelphia.

125:1-34.

4 . S a n d j a j a B . Pa r a s i t o l o g i Ke d o k t e r a n .

Helmintologi Kedokteran. Jakarta: Prestasi

Pustaka; 2007.

Natadisastra, D., Agoes, R. Parasitologi

Kedokteran: ditinjau dari organ tubuh yang

diserang. EGC, Jakarta. 2005.

Hariyanto, M.E., 2007. 'Pemanfaatan Air

Sungai dan Infeksi Schistosoma Japonicum

di Napu Poso Sulawesi T engah T ahun Jurnal

Kesehatan Masyarakat Nasional. 2006. 1 (5):

-225. Kesehatan Masyarakat Nasional .

1 (5): 219-225.

7 . G a r c i a L . S , B r u c k n e r D. A . D i a g n o s t i c

Parasitologi kedokteran. Jakarta: Penerbit

Buku Kedokteran EGC; 1996. p. 256-72.

Tjay , T an Hoan & Rahardja, Kirana. Obat-obat

penting: khasiat, penggunaan dan efek-efek

sampingnya. Elex Media Komputindo. 2007.

Luknanto, D, Model Matematika, Bahan Kuliah

Hidraulika Komputasi, Jurusan T eknik Sipil FT

UGM, Y ogyakarta. 2003.

Mayer , J. walter . Concepts of mathematical

modeling. Mcgrow-hill book company. New

Y ork. 1985.

1 . A n t o n , H . A l j a b a r L i n i e r E l e me n t e r,

T erjemahan oleh Pantur Silaban.. Jakarta.

Erlangga.

Campbell, S.L., & Haberman, R. Introduction to

Differensial Equitions with Dinamycal System.

New Jersey: Princeton University Pree. 2008.

Finizio, J. & Lads, T . Persamaan Differensial

Biasa dengan penerapan Modern. Alih Bahasa

oleh Widiarti Santoso. 1982.

Boyce, W.E. and Diprima R.C. Elementary

Differential Equation and Boundary Value

th

Problem, 6 ed. United States of America, 1996.

Naidu, D.S.,. Optimal control system.CRC,

London. 2002.


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