Qualitative and Quantitative Analyses of COVID-19 Dynamics

Faniran, Taye Samuel Nkamba Leontine Nkague Manga Thomas Timothee

COVID-19 is a highly contagious disease which has spread across the world. A deterministic model that considers an important component of individuals with vertically transmitted underlying diseases (high-risk susceptible individuals), rather than the general public, is formulated in this paper. We also consider key parameters that are concerned with the disease. An epidemiological threshold, R0, is computed using next-generation matrix approach. This is used to establish the existence and global stability of equilibria. We identify the most sensitive parameters which effectively contribute to change the disease dynamics with the help of sensitivity analysis. Our results reveal that increasing contact tracing of the exposed individuals who are tested for COVID-19 and hospitalizing them, largely has a negative impact on R0. Results further reveal that transmission rate between low-risk/high-risk susceptible individuals and symptomatic infectious individuals β and incubation rate of the exposed individuals σ have positive impact on R0. Numerical simulations show that there are fewer high-risk susceptible individuals than the general public when R0<1. This may be due to the fact that high-risk susceptible individuals may prove a bit more difficult to control than the low-risk susceptible individuals as a result of inherited underlying diseases present in them. We thus conclude that high level of tracing and hospitalizing the exposed individuals, as well as adherence to standard precautions and wearing appropriate Personal Protective Equipment (PPE) while handling emergency cases, are needed to flatten the epidemic curve.