Mathematical Model For Transmission and Control of Covid-19 In Human Population. - Marahi, Brian (Kabale University, 2024)
In this study, we propose and investigate a generalized model that describes the transmission dynamics of COVID-19 Virus Disease in humans. The transmission process from humans to humans and contaminated environment to humans is modeled by the SEIR model which covers many special cases. We show that at a particular point in time, if the product of the population growth rate r - "and the sum of the natural death rate and the number of infected people (weighted by the exposure rate) is greater than the product of the basic reproduction number and the number of susceptible individuals, then the endemic equilibrium point will be stable and the disease will persist in the population that is if,((µ+ {JI*)> RoS *). Furthermore, we show that if the product of the infection rate, the exposure rate, {J, and the population growth rater is less than the product of the sum a+µ, and 6 + y +µthen the disease-free equilibrium will be stable (that is; a~r < (a + )(0 + y + ), where 8, y are the disease-induced death rate and recovery rates, respectively). This condition then implies that the disease can be eradicated from the population.