IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X. Volume 8, Issue 6 (Nov. – Dec. 2013), PP 48-56 www.iosrjournals.org www.iosrjournals.org 48 | Page A Mathematical Model of Dracunculiasis Epidemic and Eradication Matthew O. Adewole 1 , Akindele A. Onifade 2 1,2 Department of Mathematics, University of Ibadan, Ibadan, Nigeria. Abstract: We present a mathematical model for the spread of dracunculiasis with focus on three populations; human, vector and parasite. The reproductive number is obtained from next generation matrix and the stability analyses of disease-free and endemic equilibria are conducted. Simulation of the model is presented by solving the systems of the differential equations to explore the behaviour of the model using maple 14. The paper also analyzes key parameters to determine the effective intervention. The result of this paper shows that reducing the parasite birth rate is more effective than water treatment. Keywords:Copepod, dracunculiasis, reproductive number, stability. I. Introduction Dracunculiasis (Dracontiasis), more generally called Guinea Worm Disease (GWD), is a serious problem in various countries in Africa. It is a parasitic infection acquired by drinking water from ponds contaminated by cyclopoid copepods infected with third stage larvae of the parasite Dracunculusmedinensis. Worm emergence is through the skin after a year of entering the infected person and this is usally associated with secondary bacterial infection. It has been called a neglected disease of neglected people since it strikes remote farming populations who have been passed over by national development efforts [1]. Intervention and prevention techniques have been implemented in endemic areas to significantly reduce outbreaks. Dracunculiasis is a disease of poor rural communities where the population often has to obtain drinking water from ponds infested with water fleas called Cyclops. Guinea worm eggs are not directly infective to humans. They can remain active in water for about three days and die unless they are swallowed by a cyclops. Inside the cyclops, the guinea-worm larvae develop over a period of about two weeks into a larval stage that is infective to humans [2]. The Cyclops become inactive after infection and die early [3]. There are no symptoms during the year long incubation period. High susceptibility to tetanus through ulcers caused by the emerging worms in addition to habitual abortion in some pregnant women [4] has been associated with guinea-worm diseases. When the adult worms are immersed in water, they release hundreds of thousands of mature larvae to begin the cycle anew. Each infection lasts only one year, but more than one guinea worm may emerge simultaneously or sequentially over the course of weeks, depending on the number and intensity of infection the preceding year. Humans do not develop immunity, and there is no cure or vaccine for the infection. However, the worm can be removed by physically pulling the worm out which may take up to two months to complete as worm can grow up to a meter in length and only 1-2cm can be removed per day [5]. Dracunculiasis can only be prevented by teaching persons to always filter drinking water from unsafe sources through a fine cloth and to avoid entering such sources when they have a worm emerging or about to emerge from their bodies, by treating contaminated water with ABATE larvicide (temephos; BASF, Mount Olive, NJ) or by providing safe drinking water from underground sources. Considerable progress has been made since 1986 in reducing the annual numberof reported dracunculiasis cases. The 1991 world health assembly (WHA) goal to eradicate dracunculiasis globally by 1995 was not achieved because of the limited funding available from international organization for support of technical and financial assistance to countries with endemic disease, and the limited time (4years) to meet the WHA goal [6]. In 2004, WHA established a new target date of 2009 for global eradication [7] despite considerable progress, that target also was not met, nevertheless, progress towards eradication continues. The number of cases of dracunculiasis worldwide reported by disease endemic countries to WHO and partner organizations decreased by 41 percent, from 1,797 cases in 2010 to 1,058 in 2011. As of June 2012, dracunculiasis remained endemic in four countries (Chad, Ethiopia, Mali and South Sudan [7]. The 395 cases reported and 219 villages reporting cases globally during January to June 2012 represent reductions of 51% and 39%, respectively, from the 807 cases reported and 358 villages that reported cases during January to June 2011. Of the 395 cases reported during January to June 22012, 99% were from South Sudan [7]. Few researchers have contributed towards the mathematical study of the eradication of dracunculiasis (guinea worm) diseases.Adetunde [8] investigated the current pattern of dracunculiasis disease in the Northern region of Ghana. He analysed the data from the region and wrote a time series model for the purpose of prediction. From his analysis it was observed that the number of Guinean infection cases reduce with time and