Mathematical Model for the Transmission of P. Falciparum and P. Vivax Malaria along the Thai-Myanmar Border
The most Malaria cases are occur along Thai-Mynmar border. Mathematical model for the transmission of Plasmodium falciparum and Plasmodium vivax malaria in a mixed population of Thais and migrant Burmese living along the Thai-Myanmar Border is studied. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible, infected, dormant and recovered subclasses. The loss of immunity by individuals in the infected class causes them to move back into the susceptible class. The person who is infected with Plasmodium vivax and is a member of the dormant class can relapse back into the infected class. A standard dynamical method is used to analyze the behaviors of the model. Two stable equilibrium states, a disease-free state and an epidemic state, are found to be possible in each population. A disease-free equilibrium state in the Thai population occurs when there are no infected Burmese entering the community. When infected Burmese enter the Thai community, an epidemic state can occur. It is found that the disease-free state is stable when the threshold number is less than one. The epidemic state is stable when a second threshold number is greater than one. Numerical simulations are used to confirm the results of our model.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327494Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1548
 WHO: World Malaria Situation in 1994: Weekly Epidemiological Record. Geneva 1997
 M. Mayxay, S. Pukrittayakamee, P. N. Newton, and N. J. White, "Mixed-Species malaria infections in humans", Trends in Parasitology. 2004, vol. 20, pp. 233-240.
 PC. C. Garnhan, Malaria parasites of man: life-cycles and morphology (excluding unltrastructure. In Malaria, edited by Wernsdorfer WH, McGregor I. Edinburgh: Churchill Livingstone; 1988.
 R. N. Price, T. Emiliana, C. A. Guerra, S. Yeung, N. J. White, and N. M. Anstey, "Vivax Malaria: Neglected and Not Benign", Am J Trop Med Hyg 2007, vol. 77, pp. 79-87.
 C. Wongsrichanalai, J. Sirichaisinthop, J. J. Karwacki, K. Congpuong, S. R. Miller , L. P. Thimasarn , and K. Thimasarn , "Drug Resistant Malaria on the Thai-Myanmar and Thai-Cambodian Borders.", SEA J Trop Med Pub Health 2001, vol. 32, pp. 41-49.
 S. Pinichpongse, "The Current Situation of the Anti-Malaria Programme in Thailand.", Preceeding of the Asia and Pacific Conference on Malaria, Honolulu, Hawaii 1985, pp. 92-98.
 Annual Epidemiological Surveillance Report. Division of Epidemiology, Ministry of Public Health, Royal Thai Government; 1965-2006.
 B. Sina, "Focus on Plasmodium Vivax.", Trends in Parasitology 2002, vol. 18, pp. 287-289
 R. M. Anderson , and R. M. May, Infectious Disease of Humans, Dynamics and Control. Oxford: Oxford University Press; 1991.
 A. Kammanee, N. Kanyamee, and I. M. Tang, " Basic Reproduction Number for the Transmission of Plasmodium Vivax Malaria.", SEA J Trop Med Pub Health 2001, vol. 32, pp. 702-706.
 R. Ross, The prevention of malaria. 2nd ed. London: John Murray; 1911.
 G. MacDonald , The epidemiology and control of malaria. London: Oxford University Press; 1957.
 L. Esteva , and C. Vargas , " Analysis of a dengue disease trasmission model.", Math. Bioscience 1998, vol. 150: 131-151.
 J. E. Marsden, and M. McCracken, The Hopf Bifurcation and its application. New York: Springer-Verlag;1976.