Stability and Numerical Investigation of modified SEIR model with Vaccination and Life-long Immunity
European Journal of Molecular & Clinical Medicine,
2020, Volume 7, Issue 3, Pages 3034-3044
AbstractIn understanding the spread and control of infectious diseases, mathematical modelling has become an important instrument. The epidemic disease COVID-19 caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) has affected the population of almost all the countries. This disease is highly contagious and spreads through one to one contact (physical closeness). It spreads through the air in the form of tiny droplets transmitted by the breath, cough, sneezing, or even verbal contact of an infected person . Being highly contagious and mortality rate, the number of confirmed cases and deaths are alarmingly rising. By routinely washing hands, keeping unwashed hands away from the face, avoiding public areas, and maintaining social distance, the various strategies to curb the spread include ensuring adequate hygiene. As a consequence, aggressive measures are required to control the spread of infectious diseases, particularly those for which both vaccines and treatments are available. Besides, combating the occurrence of a disease is always easier than treating it. This paper formulates and solves numerically the modified SEIR model with vital dynamics includes an additional compartment called Vaccination with an assumption that the vaccination will provide lifelong immunity. This assumption is feasible as the immunity can be extended through booster vaccinations in due course. The basic reproduction number is calculated and the stability of the model is discussed using the Lyapunov method. The importance of the various epidemiological parameters related to the Vaccination compartment model is discussed numerically also.
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