A Mathematical Model for Stability Analysis of Covid like Epidemic/Endemic/Pandemic

Abstract

The transmission and spread of infectious disease like Covid-19 occurs through horizontal and vertical mode. The causative pathogens for such kind of disease may be bacterium, protozoa, virus or toxin. The infectious diseases like AIDS, SARS, MARS, Polio Plague, Bubonic Plague and Covid-19 have destroyed the social and economic structure of world population. The world scientific community adopts different mechanisms to model and analyse the population dynamics of infectious disease outbreaks. Mathematical Modelling is the most effective tool to take the informed decision about the containment, control and eradication of the pandemic. The main focus of Government and public health authorities is to design the strategy in destabilising the spread and impact of the infections. A series of models-SIR, SEIR, SEIRD, SEAIHCRD, SAUQAR has been under study to combat the Covid-19 since its inception. An effort has been made to design the model based on reproduction number, endemic equilibrium and disease-free equilibrium to curtail the impact of Covid-19 through stability analysis methods-Hurwitz stability criteria, Lyapunov Method and Linear Stability Analysis.