Dynamical Modeling and COVID-19 Pandemic

The world health organization (WHO) has declared the Coronavirus (COVID-19) a pandemic in 2020. Considering this ongoing global issue, different health and safety measure has been recommended by the WHO to ensure the proactive, comprehensive, and coordinated steps to bring back the whole world into a normal situation. There are around 100 plus research groups across the world trying to develop a vaccine for previous and new versions of coronavirus. All the work is at an early stage, contains huge uncertainties and a long list of unanswered questions however, continuous efforts lead to success. Therefore, the quantitative and qualitative analysis of the COVID–19 pandemic is needed for the identification and controlling the spread of COVID-19. Mathematical models with computational simulations are the effective tools that help global efforts to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates. In this chapter, we develop two simple models for coronavirus disease spreading within a mathematically/biologically feasible region, i.e., positively invariant for the model and boundedness solution of the system. So that the system becomes well-posed mathematically and epidemiologically for sensitive (stability) analysis. Then computational results show the occurrence of a forward bifurcation when the basic reproduction number is equal to unity. The proposed method gives a major step forward to evaluate the models and identify the key critical parameters, i.e., recovery factors. These critical model-parameters allow the biologist/chemist to specify/distinguish control strategies to adopt further precaution measures with improvements. This is another way of controlling the individuals from the spreading called control monitoring strategy. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.