scholarly journals Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Resistance

2017 ◽  
Author(s):  
Maxwell G. De Jong ◽  
Kevin B. Wood
Keyword(s):  
Drug Resistance ◽  
Spatial Heterogeneity ◽  
Selection Pressure ◽  
First Passage Time ◽  
Passage Time ◽  
Spatial Profile ◽  
Drug Dosing ◽  
Spatial Gradients ◽  
Resistance Evolution ◽  
Dosing Strategies

Spatial heterogeneity plays an important role in the evolution of drug resistance. While recent studies have indicated that spatial gradients of selection pressure can accelerate resistance evolution, much less is known about evolution in more complex spatial profiles. Here we use a stochastic toy model of drug resistance to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. Interestingly, there exists an intermediate regime—characterized by comparable rates of migration and mutation—in which the rate of fixation can be either accelerated or decelerated depending on the spatial profile, even when spatially averaged selection pressure remains constant. Finally, we demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Our results may lay the groundwork for optimized, spatially-resolved drug dosing strategies for mitigating the effects of drug resistance.

scholarly journals Antimalarial mass drug administration in large populations and the evolution of drug resistance

2021 ◽  
Author(s):  
Tran Dang Nguyen ◽  
Thu Nguyen-Anh Tran ◽  
Daniel M. Parker ◽  
Nicholas J White ◽  
Maciej F Boni
Keyword(s):  
Drug Resistance ◽  
Case Management ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Selection Pressure ◽  
Diagnosis And Treatment ◽  
Drug Resistant ◽  
High Coverage ◽  
Resistance Evolution ◽  
Large Populations

AbstractMass drug administration (MDA) with antimalarials has been shown to reduce prevalence and interrupt transmission in small populations, in populations with reliable access to antimalarial drugs, and in populations where sustained improvements in diagnosis and treatment are possible. Effective MDA eliminates drug-resistant parasites which has the long-term benefit of extending the useful therapeutic life of first-line therapies for all populations, not just the focal population where MDA was carried out. However, in order to plan elimination measures effectively, it is necessary to characterize the conditions under which failed MDA could exacerbate resistance. We use an individual-based stochastic model of Plasmodium falciparum transmission to evaluate this risk in large populations (>40K) where access to antimalarial treatments may not be uniformly high and where re-importation of drug-resistant parasites may be common. We find that drug-resistance evolution can be accelerated by MDA when all three of the following conditions are met: (1) strong genetic bottlenecking that falls short of elimination, (2) re-importation of resistant genotypes, and (3) continued selection pressure during routine case management post-MDA. Accelerated resistance levels are not immediate but follow the rebound of malaria cases post-MDA, if this is allowed to occur. Crucially, resistance is driven by the selection pressure during routine case management post-MDA and not the selection pressure exerted during the MDA itself. Second, we find that increasing treatment coverage post-MDA increases the probability of local elimination in low-transmission regions (PfPR < 2%) in scenarios with both low and high levels of drug-resistance importation. This emphasizes the importance of preparation and planning to ensure that MDA has a high probability of leading to elimination, and the necessity of supporting public health infrastructure to provide high coverage of diagnosis and treatment post-MDA.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

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