A model for the emergence of drug resistance in the presence of asymptomatic infections

Abstract

An analysis of a mathematical model, which describes the dynamics of an aerially transmitted disease, and the effects of the emergence of drug resistance after the introduction of treatment as an intervention strategy is presented. Under explicit consideration of asymptomatic and symptomatic infective individuals for the basic model without intervention the analysis shows that the dynamics of the epidemic is determined by a basic reproduction number R0. A disease-free and an endemic equilibrium exist and are locally asymptotically stable when R0<1 and R0>1 respectively. When treatment is included the system has a basic reproduction number, which is the largest of the two reproduction numbers that characterise the drug-sensitive (R1) or resistant (R2) strains of the infectious agent. The system has a disease-free equilibrium, which is stable when both R1 and R2 are less than unity. Two endemic equilibria also exist and are associated with treatment and the development of drug resistance. An endemic equilibrium where only the drug-resistant strain persists exists and is stable when R2>1 and R1<R2. A second endemic equilibrium exists when R1>1 and R1>R2 and both drug-sensitive and drug-resistant strains are present. The analysis of the system provides insights about the conditions under which the infection will persist and whether sensitive and resistant strains will coexist or not.