A Study Focusing on Singularly Perturbative Behaviour of Nonlinear Advection–Diffusion-Reaction Processes
The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.
https://doi.org/10.1140/epjp/s13360-024-04894-w
Mathematical Modelling of Antibiotic Interaction on Evolution of Antibiotic Resistance: An Analytical Approach
The emergence and spread of antibiotic-resistant pathogens have led to the exploration of antibiotic combinations to enhance clinical effectiveness and counter resistance development. Synergistic and antagonistic interactions between antibiotics can intensify or diminish the combined therapy’s impact and evolve as bacteria transition from wildtype to mutant (resistant) strains. Experimental studies have shown that the antagonistically interacting antibiotics against wildtype bacteria slow down the evolution of resistance. Interestingly, other studies have shown that antibiotics that interact antagonistically against mutants accelerate resistance. However, it is unclear if the beneficial effect of antagonism in the wildtype bacteria is more critical than the detrimental effect of antagonism in the mutants. This study aims to illuminate the importance of antibiotic interactions against wildtype bacteria and mutants on the deacceleration of antimicrobial resistance.
To address this, a mathematical model that explores the population dynamics of wildtype and mutant bacteria under the influence of interacting antibiotics is developed and analyzed. The model investigates the relationship between synergistic and antagonistic antibiotic interactions with respect to the growth rate of mutant bacteria acquiring resistance.
https://doi.org/10.7717/peerj.16917
