15 research outputs found
Understanding Biofilm-Phage Interactions in Cystic Fibrosis Patients Using Mathematical Frameworks
When planktonic bacteria adhere together to a surface, they begin to form
biofilms, or communities of bacteria. Biofilm formation in a host can be
extremely problematic if left untreated, especially since antibiotics can be
ineffective in treating the bacteria. Certain lung diseases such as cystic
fibrosis can cause the formation of biofilms in the lungs and can be fatal.
With antibiotic-resistant bacteria, the use of phage therapy has been
introduced as an alternative or an additive to the use of antibiotics in order
to combat biofilm growth. Phage therapy utilizes phages, or viruses that attack
bacteria, in order to penetrate and eradicate biofilms. In order to evaluate
the effectiveness of phage therapy against biofilm bacteria, we adapt an
ordinary differential equation model to describe the dynamics of phage-biofilm
combat in the lungs. We then create our own phage-biofilm model with ordinary
differential equations and stochastic modeling. Then, simulations of parameter
alterations in both models are investigated to assess how they will affect the
efficiency of phage therapy against bacteria. By increasing the phage mortality
rate, the biofilm growth can be balanced and allow the biofilm to be more
vulnerable to antibiotics. Thus, phage therapy is an effective aid in biofilm
treatment
Stability and Hopf bifurcation of a two species malaria model with time delays
We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values
The dynamics of multiple species and strains of malaria
This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasi-endemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion