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

Sriwahyuni Sriwahyuni, Rina Ratianingsih, Hajar Hajar


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.


optimal control; Pontryagin minimum principle; Schistosoma japonicum


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