The dynamics of bacterial infection, innate immune response, and antibiotic treatment

Mudassar Imran,Hal L Smith

doi:10.3934/dcdsb.2007.8.127

Abstract

We develop a simple mathematical model of a bacterial colonization of host tissue which takes account of nutrient availability and innate immune response. The model features an infection-free state which is locally but not globally attracting implying that a super-threshold bacterial inoculum is required for successful colonization and tissue infection. A subset $B$ of the domain of attraction of the disease-free state is explicitly identified. The dynamics of antibiotic treatment of the infection is also considered. Successful treatment results if the antibiotic dosing regime drives the state of the system into $B$.

Highlights

Mathematical modeling of the effects of drug treatment has long been used side-by-side with experimental studies [2, 5, 7, 8, 21, 24, 33]
Most mathematical models of the effects of antimicrobial agents on bacterial populations assume that bacteria grow at an exponential rate in the absence of the antimicrobial agent [22, 13] or assume logistic growth of bacteria in the absence of treatment [2, 21, 14]
We show that dosing regimes that drive down bacterial density to sufficiently low levels will allow phagocyte levels to recover to super-threshold levels and thereby achieve successful treatment

Summary

Introduction

Mathematical modeling of the effects of drug treatment has long been used side-by-side with experimental studies [2, 5, 7, 8, 21, 24, 33]. Most mathematical models of the effects of antimicrobial agents on bacterial populations assume that bacteria grow at an exponential rate in the absence of the antimicrobial agent [22, 13] or assume logistic growth of bacteria in the absence of treatment [2, 21, 14]. This seems surprising given that in vitro experiments often use the chemostat [9, 22] and many researchers point out that levels of certain key nutrients are critical to successful colonization of tissue by pathogens. Simulations explore various features of drug treatment including both successful and unsuccessful treatment regimes

Model of Infection Process

Antibiotic Treatment

Findings

Antibiotic Treatment Simulations