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

Modeling the Impact of Misinformation on the Transmission Dynamics of COVID-19

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model’s potential to develop effective strategies for combating misinformation related to COVID-19

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