The transmission model of P.falciparum and P.vivax malaria between Thai and Burmese

Abstract

The transmission of Plasmodium falciparum and Plasmodium vivax malaria of Thais and Burmese is studied through a mathematical model. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible and infectious subclasses. The loss of immunity by individuals in the infectious class causes them to move back into the susceptible class. Standard dynamical method is used to analyze the behavior 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 into the community. When there are infected Burmese enters into the Thai community, the epidemic state can occur. It is found that the disease free state is stable when the threshold number R0 is less than one. The epidemic state is stable when RET and REB (where these threshold numbers are for the individual populations) are greater than one. The numerical simulations of our model illustrate what the results would be for our theoretical model.