A model for transmission of partial resistance to anti-malarial drugs

Anti-malarial drug resistance has been identified in many regionsfor a long time. In this paper we formulate a mathematical model ofthe spread of anti-malarial drug resistance in the population.The model is suitable for malarial situations in developingcountries. We consider the sensitive and resistant strains ofmalaria. There are two basic reproduction ratios corresponding tothe strains. If the ratios corresponding to the infections of thesensitive and resistant strains are not equal and they are greater than one,then there exist two endemic non-coexistent equilibria. In the casewhere the two ratios are equal and they are greater than one, the coexistenceof the sensitive and resistant strains exist in the population. Itis shown here that the recovery rates of the infected host and theproportion of anti-malarial drug treatment play important roles inthe spread of anti-malarial drug resistance. The interestingphenomena of ''long-time' coexistence, which may explain the realsituation in the field, could occur for long period of time whenthose parameters satisfy certain conditions. In regards to controlstrategy in the field, these results could give a good understandingof means of slowing down the spread of anti-malarial drugresistance.