Modeling induced resistance to plant disease using a dynamical systems approach

Plants present a rich source of nutrients for many organisms, making it a target for herbivores and infectious agents. Plants, though lacking a proper immune system, have developed an array of constitutive and inducible defenses to fend off these attacks.

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Microbe-plant interactions represent a dynamic spectrum of associations shaped by intricate chemical signaling. These interactions can be neutral, beneficial, or detrimental, and profoundly influence plant physiology, growth, and ecosystem function. The plant microbiome, comprising bacteria, fungi, archaea, protists, and viruses, plays a pivotal role in mediating these effects through surface colonization, internal colonization, or systemic symbiosis.Mutualistic associations, particularly with...

Pharmacodynamic models are essential tools in understanding the relationship between drug concentrations and their effects on biological systems. By characterizing the dynamics of drug action, these models guide dose selection, optimize therapeutic efficacy, and inform the development of new drugs. Two major classes of pharmacodynamic models include direct effect and indirect response models.Direct Effect ModelsDirect effect models describe the immediate relationship between drug concentration...

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...