A mathematical model of mobility-related infection and vaccination in an epidemiological case.

ABSTRACT

In this study, we established a system of differential equations with piecewise constant arguments to explain the impact of epidemiological transmission between different locations. Our main goal is to look into the need for vaccines as well as the necessity of the lockdown period. We proved that keeping social distance was necessary during the pandemic spread to stop transmissions between different locations and that re-vaccinations, including screening tests, were crucial to avoid reinfections. Using the Routh-Hurwitz Criterion, we examined the model's local stability and demonstrated that the system could experience Stationary and Neimark-Sacker bifurcations depending on certain circumstances.

Modeling a SEIVRS dynamic behavior with transportation-related transmissionEstablishing a system of two urban as differential equations with piecewise constant argumentsStability analysis of disease-free and co-existing equilibrium pointsAnalyzing bifurcation types around the disease-free and co-existing equilibrium points.Illustrating numerical scenarios that were applied during the pandemic event.