Pharma Focus Asia

Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis

John Fors, Natasha Strydom, William S. Fox, Ron J. Keizer, Radojka M. Savic


Standard treatment for active tuberculosis (TB) requires drug treatment with at least four drugs over six months. Shorter-duration therapy would mean less need for strict adherence, and reduced risk of bacterial resistance. A system pharmacology model of TB infection, and drug therapy was developed and used to simulate the outcome of different drug therapy scenarios. The model incorporated human immune response, granuloma lesions, multi-drug antimicrobial chemotherapy, and bacterial resistance. A dynamic population pharmacokinetic/pharmacodynamic (PK/PD) simulation model including rifampin, isoniazid, pyrazinamide, and ethambutol was developed and parameters aligned with previous experimental data. Population therapy outcomes for simulations were found to be generally consistent with summary results from previous clinical trials, for a range of drug dose and duration scenarios. An online tool developed from this model is released as open source software. The TB simulation tool could support analysis of new therapy options, novel drug types, and combinations, incorporating factors such as patient adherence behavior.


Standard treatment for active pulmonary infection with Mycobacterium tuberculosis (TB) usually involves lengthy therapy based on four different drugs taken over 6 months. Adherence has been shown to be a major predictor of treatment failure and shorter-duration therapy has been suggested to lower risk of treatment failure and bacterial resistance [1–4].

Pharmacokinetic/pharmacodynamics (PK/PD) mathematical models for TB have mostly focused on short-term drug effects during the initial ten days of treatment rather than overall therapy outcome. Most earlier in-vitro experiments and in-silico simulations of TB drug effectiveness have been based on monodrug therapy, even though standard patient treatment for TB involves four or more drugs. Further, previous simulation models often have been relatively deterministic, and done at individual patient level, thus offering limited ability to assess therapy outcomes on a broader population basis [5–7].

Materials and methods

The model building process did not include studies with human participants, animals or field work performed by any of the authors and did not require ethics approval.

Bacterial infection and growth

Pulmonary infection is assumed to be transmitted through aerosolized droplets containing M. tuberculosis bacteria. Once in the lung, characterized by our model as extracellular space, bacteria penetrate into alveolar macrophages, where they proceed to grow according to rates characteristic for pulmonary tuberculosis. In line with the originally validated model from Marino et al., 2004 uncontrolled infection with M. tuberculosis eventually results in sustained high bacterial density, both outside and inside of macrophages, often reaching maximum levels of 107 to 109 CFU/mL in the lung compartments, after 100 to 200 days from initial infection. Sustained infection may trigger a complex host immune-bacteria reaction leading to formation of encapsulation of infected tissues. The inflamed tissue forms nodules, and may grow to become larger granulatomous lesions. Here the immune system is actively sequestering the infection into lesions to help prevent further spread of bacteria. If no immune system was on board the infection would grow further without stopping, S6 Fig. A major contribution of the immune effect in our model is to simulate the environment of lung lesions and provide the necessary barrier to drug diffusion that we expect from macrophages and other immune cells. The lesions can be considered a distinct compartment, and may contain substantial concentrations of bacteria. The integrated disease model and immune model compartments are illustrated in Fig 14 [30].


This study presented an integrated systems pharmacology model and simulation tool to support prediction of outcomes of different therapies for pulmonary tuberculosis infection. The simulation model allows rapid and flexible assessment of impact of various drug therapy and population parameters, such as drug selection, drug dose and dosing patterns, multi-dose combinations, and therapy start time and duration.


We would like to thank Klaus Romero and Alexander Berg from the Critical Path to TB Drug Regimens Initiative (CPTR) for their valuable discussion and support throughout this project.
Citation: Fors J, Strydom N, Fox WS, Keizer RJ, Savic RM (2020) Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis. PLoS Comput Biol 16(8): e1008107.

Editor: James Gallo, University at Buffalo - The State University of New York, UNITED STATES

Received: September 5, 2019; Accepted: June 30, 2020; Published: August 18, 2020

Copyright: © 2020 Fors et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All source code and parameter data can be found at and the web application is available at

Funding: This work was supported by the US National Institutes of Health (NIH) grants R01AI106398-01 (to RS) and Critical Path to TB Drug Regimens (CPTR) Initiative, Bill and Melinda Gates Foundation, grants OPP1031105 and Grand Challenges in Global Health-11 (to RS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: RJK is a stock owner, co-founder and chief scientific officer of InsightRX. The remaining authors have no conflicts of interest to declare.

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