Abstract
•The epicenter of COVID-19 keeps shifting to the south.•Coexisting HIV & COVID-19 is a worry for southern hemisphere countries.•Stability analysis is provided for a HIV-COVID-19 simple model.•Existence of backward and forward bifurcations is shown.•Predicted prevalence from a generalized COVID-19 model is given.
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?