Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model

Abstract

Coronavirus can be transmitted through the things that people carry or the things where it sticks to after being spread by the sufferer. Instead, various preventive measures have been carried out. We create a new mathematical model that represents Coronavirus that exists in non-living objects, susceptible, and infected subpopulations interaction by considering the Coronavirus transmission through non-living objects caused by susceptible and infected subpopulations along with its prevention to characterize the dynamics of Coronavirus transmission in the population under those conditions. One disease-free and two infection equilibrium points along with their local stability and coexistence are identified. Global stability of the disease-free equilibria and basic reproduction number are also investigated. Changes in susceptible-Coronavirus interaction rate generate Fold and Hopf bifurcations which represent the emergence of a cycle and the collision of two infection equilibrium points respectively. Catastrophe generated by the collision between an attractor and a repeller is found around a Generalized Hopf bifurcation point by changing susceptible-Coronavirus interaction rate and increasing rate of Coronavirus originating from infected subpopulation. It represents a momentary unpredictable dynamics as the effect of Coronavirus addition and infection. Non-chaotic strange attractors that represent complex but still predictable dynamics are also triggered by Generalized Hopf bifurcation when the susceptible-Coronavirus interaction rate and one of the following parameters, i.e. increasing rate of Coronavirus originating from infected subpopulation or infected subpopulation recovery rate vary.