The dynamics of drug action on the within-host population growth of infectious agents: Melding pharmacokinetics with pathogen population dynamics

Abstract

The use of simple mathematical models to study the kinetics of drug action and decay within vertebrate hosts has a long history with a major objective being to derive drug dosage regimens that optimize efficacy and minimize toxicity to the patient. Mathematical models of the relationship between dosage, route of delivery, drug concentration in defined sites and effect on a particular pathogen are widely used in the pharmacological literature. A more recent literature is that concerned with the population dynamics of pathogen replication within the host subjected to pressures exerted by the human immune system. In this paper we develop a theoretical framework to meld both approaches with the aim of identifying threshold criteria that dictate the optimum pattern of drug administration for pathogen clearance from the host. In particular we show how the percentage reduction in microparasite abundance is related to the pharmacokinetic parameter, AUC, recording the area under the drug concentration-time curve within the treated patient, in terms of the parameters that define the population dynamics of the pathogen and the properties of the drug. Two particular pathogens are examined to illustrate the principles underpinning the dynamics of the pharmacokinetic-population dynamic models, namely HIV and Plasmodium falciparum. Criteria for pathogen persistence or elimination are derived for these specific models based on the definition of a basic reproductive number, R0, which measures the average number of secondary infected target cells in a host generated by a single infected cell (CD4 lymphocyte for HIV, and erythrocyte for P. falciparum) within a population of susceptible cells. For the pathogen to invade the host and persist over time, R0≤ 1. Under chemotherapeutic regimens, expressions for Re are derived allowing estimates to be made of the ideal treatment regime required to eliminate the pathogen, both for HIV and P. falciparum malaria.