Title: A model for the emergence of drug resistance in the presence of asymptomatic infections
Citation: MATHEMATICAL BIOSCIENCES vol. 243 no. 2 p. 163-177
Publication Year: 2013
JRC N°: JRC65564
ISSN: 0025-5564
URI: http://www.sciencedirect.com/science/article/pii/S0025556413000758
DOI: http://dx.doi.org/10.1016/j.mbs.2013.03.003
Type: Articles in periodicals and books
Abstract: An analysis of a mathematical model, which describes the transmission dynamics of an epidemic, 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. In the case of influenza, for acquired immunity lasting up to several years, the model’s intrinsic damped oscillations can resonate with an annually forced seasonal stimulus. 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 exists when R2 > 1 and where only the drug resistant strain is present. A second endemic equilibrium exists when R1 > 1 and R2 < R1 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.
JRC Directorate:Space, Security and Migration

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