Modeling in mathematics in estimation and prediction of the coronavirus infections in Kitui county. A case with isolation of the vulnerable

Abstract

People’s lives have been affected socially by the coronavirus around the globe. Because of its social and economic impact, some measures for the prevention of the disease have been placed so that the spread can reduce. Quarantine, social distancing, and social distancing are some of the control measures. One that is considered to be very effective is for the vulnerable population to be isolated. A Model including six compartments was developed so that the number of people recovering may increase, so to achieve this vulnerable population was isolated. These six compartments are namely below; Susceptible, Exposed, Infected, Quarantined, Isolation of Vulnerable, and Recovered. Formulation of endemic equilibrium points, disease-free equilibrium, and local stability of disease-free equilibrium were theoretically proved. By use of the next generation matrix, derivation of basic reproductive number which is abbreviated as Rₒ was done. There is THE stability of disease-free equilibrium which is also abbreviated as a disease-free equilibrium when the basic reproductive number is less than one, which is 𝑹𝟎 < 𝟏. There is the stability of endemic equilibrium, the endemic equilibrium point when the basic reproductive number is greater than one, which is 𝑹𝟎 > 𝟏. There is instability in disease-free equilibrium when 𝑹𝟎 > 𝟏. Susceptible, Exposed, Infected, Isolated Vulnerable and Recovered population model was solved numerically by Runge Kutta 4th order; the drawn graphs also showed that when the vulnerable population is isolated there is an increment in the number of people who recover and a reduction in deaths. More isolation Centers so as to isolate vulnerable populations to recover more is recommended whereby the world health organization and ministry of health in Kenya need to put it in place.