ABSTRACT
Were southern hemisphere countries right to undertake national lockdown during their summer time? Were they right to blindly follow the self-isolation wave that hit European countries in full winter? As a southern hemisphere country like South Africa stands now as the most COVID-19 and HIV affected country in Africa, we use in this paper, recent COVID-19 data to provide a statistical and comparative analysis that may alert southern hemisphere countries entering the winter season. After that, we use a generalized simple mathematical model of HIV-COVID-19 together with graphs, curves and tables to compare the pandemic situation in countries that were once the epicenter of the disease, such as China, Italy, Spain, United Kingdom (UK) and United States of America (USA). We perform stability and bifurcation analysis and show that the model contains a forward and a backward bifurcation under certain conditions. We also study different scenarios of stability/unstability equilibria for the model. The fractional (generalized) COVID-19 model is solved numerically and a predicted prevalence for the COVID-19 is provided. Recall that Brazil and South Africa share number of similar social features like Favellas (Brazil) and Townships (South Africa) with issues like promiscuity, poverty, and where social distanciation is almost impossible to observe. We can now ask the following question: Knowing its HIV situation, is South Africa the next epicenter in weeks to come when winter conditions, proven to be favorable to the spread of the new coronavirus are comfily installed?
ABSTRACT
A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.
