Bacterial load slopes represent biomarkers of tuberculosis therapy success, failure, and relapse

There is an urgent need to discover biomarkers that are predictive of long-term TB treatment outcomes, since treatment is expense and prolonged to document relapse. We used mathematical modeling and machine learning to characterize a predictive biomarker for TB treatment outcomes. We computed bacterial kill rates, γf for fast- and γs for slow/non-replicating bacteria, using patient sputum data to determine treatment duration by computing time-to-extinction of all bacterial subpopulations. We then derived a γs-slope-based rule using first 8 weeks sputum data, that demonstrated a sensitivity of 92% and a specificity of 89% at predicting relapse-free cure for 2, 3, 4, and 6 months TB regimens. In comparison, current methods (two-month sputum culture conversion and the Extended-EBA) methods performed poorly, with sensitivities less than 34%. These biomarkers will accelerate evaluation of novel TB regimens, aid better clinical trial designs and will allow personalization of therapy duration in routine treatment programs.

Species coexistence and temporal environmental fluctuations: a quantitative comparison between stochastic and seasonal variations.

Temporal environmental variations may promote diversity in communities of competing populations. Here we compare the effect of environmental stochasticity with the effect of periodic (e.g., seasonal) cycles, using analytic solutions and individual-based Monte-Carlo simulations. Even when stochasticity facilitates coexistence it still allows for rare sequences of bad years that may drive a population to extinction, therefore the stabilizing effect of periodic variations is stronger. Correspondingly, the mean time to extinction grows exponentially with community size in periodic environment and switch to power-law dependence under stochastic fluctuations. On the other hand, the number of temporal niches in periodic environment is typically lower, so as diversity increases stochastic temporal variations may support higher species richness.

Stable motifs delay species loss in simulated food webs

Some three-species motifs (unique patterns of interactions between three species) are both more stable when modeled in isolation and over-represented in empirical food webs. This suggests that these motifs may reduce extinction risk for species participating in them, ultimately stabilizing the food web as a whole. We test whether a species' time to extinction following a perturbation is related to its participation in stable and unstable motifs and assess how motif roles co-vary with a species' degree or trophic level. We found that species' motif roles are related to their times to extinction following a disturbance. Specifically, participating in many omnivory motifs (whether in absolute terms, as a proportion of the species' role, or relative to other species in the network) was associated with more rapid extinction, even though omnivory has previously been identified as a stable motif. Participating in the other three stable motifs (three-species chain, apparent competition, and direct competition) was associated with longer times to extinction. While motif roles were associated with extinction risk, they also varied strongly with degree and trophic level. This means that these simpler measures of a species' role may be sufficient to roughly predict which species are most vulnerable to disturbance, but the additional information encapsulated in a motif role can further refine predictions of vulnerability. Moreover, where researchers are a priori interested in motif roles, our results confirm that these roles can be interpreted with respect to extinction risk.

Nouveau short-course therapy and morphism mapping for clinical pulmonary Mycobacterium kansasii

Standard therapy [isoniazid, rifampin, ethambutol], with or without a macrolide, for pulmonary Mycobacterium kansasii lasts more than a year. Therefore, shorter treatment duration regimens are required. We used data from 32 Taiwanese patients treated with standard therapy who were followed using repetitive sampling-based sputum Mkn time-to-positivity in liquid cultures to calculate kill slopes [γ] based on ordinary differential equations and time-to-extinction of each patient’s bacterial burden. The γ was 0.18 [95% Confidence Interval (CI): 0.16-0.20] log10 CFU/mL/day on standard therapy. Next, we identified Mkn time-to-extinction in the hollow fiber system model of pulmonary M. kansasii disease [HFS-Mkn] treated with standard therapy, which was a γ of 0.60 [95% CI: 0.45-0.69) log10 CFU/mL/day. The γs and time-to-extinctions between the two datasets formed structure-preserving maps based on category theory: thus, we could map them from one to the other using morphisms. This mapping identified a multistep non-linear transformation-factor for time-to-extinction from HFS-Mkn to patients. Next, a head-to-head study in the HFS-Mkn identified median time-to-extinction for standard therapy of 38.7 [95% CI: 29.1-53.2) days, isoniazid-rifampin-ethambutol-moxifloxacin of 21.7 [95% CI: 19.1-25) days, isoniazid-rifampin-moxifloxacin of 22 [96% CI: 20.1-24.5) days, and rifampin-moxifloxacin-tedizolid of 20.7 [95% CI:18.5-29) days. Our transformation-factor based translation predicted the proportion of patients of 90.7 [88.74-92.35)% achieving cure with standard therapy at 12 months, and 6-months cure rates of 99.8 [95% CI: 99.27-99.95)% for isoniazid-rifampin-ethambutol-moxifloxacin, 92.2 [90.37-93.71)% for isoniazid-rifampin-moxifloxacin, and 99.9 [99.44-99.99)% for rifampin-moxifloxacin-tedizolid. Thus, rifampin-moxifloxacin-tedizolid and isoniazid-rifampin-ethambutol-moxifloxacin are predicted to be short-course chemotherapy regimens for pulmonary M. kansasii disease.

Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognize the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable; however, their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective ‘birth–death’ description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth–death framework. We show that these predictions agree very well with the results of stochastic models by analysing the simplified susceptible–infected–susceptible (SIS) dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness ( Trypanosoma brucei gambiense ).

Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population [Formula: see text]. In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate [Formula: see text], carrying capacity [Formula: see text], intensity of Gaussian noise [Formula: see text], noise intensity [Formula: see text] and stability index [Formula: see text] vary. The MET from the interval [Formula: see text] at the right boundary is finite if [Formula: see text]. For [Formula: see text], the MET from [Formula: see text] at this boundary is infinite. A larger stability index [Formula: see text] is less likely leading to the extinction of the fish population.

Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable, however their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective “birth-death” description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We show these predictions agree very well with the results of stochastic models by analysing the simplified SIS dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).