Abstract
Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.
Highlights
IntroductionThe paroxysmal stage of Pertussis is characterized by episodes of coughing with a distinctive “whooping” sound when breathing in
Pertussis commonly known as whooping cough is one of the highly communicable bacterial respiratory tract infections mainly caused by Bordetella Pertussis
When > 1, it follows that an infectious individual will cause more than one additional infection on average, and the disease will spread and the endemic equilibrium point is stable as a result of this
Summary
The paroxysmal stage of Pertussis is characterized by episodes of coughing with a distinctive “whooping” sound when breathing in This characteristic cough gives the disease its common name, Whooping Cough. There has been a resurgence of whooping cough outbreak and western countries are highly endemic despite high vaccination coverage of about 90%. Perhaps this could be that the vaccinated individuals can still become infected as a result of the disease mutation. The resurgence of whooping cough (pertussis) globally most especially in western countries with high vaccination coverage has been a concern. The optimal control strategy was developed and characterized to minimize the infected class, simulation was carried out using the Forward-backward sweep method by incorporating RK-4 method
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