Well-Posedness of a Novel Mathematical Model for Pertussis With Vaccination and Asymptomatic Classes

Abstract

Bordetella pertussis is the bacterium that causes pertussis, a highly contagious respiratory disease spread primarily through droplet coughing or sneezing. Despite all efforts to reduce or even eliminate the transmission of pertussis disease, it continues to be hazardous in newborns and adults, causing illness and death in both age groups. Numerous studies have examined the factors that influence the spread of pertussis epidemiology and have used mathematical models to predict the possible effects of different vaccination approaches. In this paper, a mathematical model of pertussis has been formulated by incorporating the vaccination and Asymptomatic classes. We established that the existence and uniqueness of solution, boundedness and positivity of solution holds for the epidemiological model.