Modeling of COVID-19 spread with self-isolation at home and hospitalized classes

This work examines the impacts of self-isolation and hospitalization on the population dynamics of the Corona-Virus Disease. We developed a new nonlinear deterministic model eight classes compartment, with self-isolation and hospitalized being the most effective tools. There are (Susceptible SC(t), Exposed E(t), Asymptomatic infected IA(t), Symptomatic infected AS(t), Self-isolation TM(t), Hospitalized TH(t), Healed H(t), and Susceptible individuals previously infected HC(t)). The expression of basic reproduction number R0comes from the next-generation matrix method. With suitably constructed Lyapunov functions, the global asymptotic stability of the non-endemic equilibria Σ0for R0<1and that of endemic equilibria Σ∗for R0>1are established. The computed value of R0=3.120277403proves the endemic level of the epidemic. The outbreak will lessen if a policy is enforced like self-isolation and hospitalization. This is related to those policies that can reduce the number of direct contacts between infected and susceptible individuals or waning immunity individuals. Various simulations are presented to appreciate self-isolation at home and hospitalized strategies if applied sensibly. By performing a global sensitivity analysis, we can obtain parameter values that affect the model through a combination of Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods to determine the parameters that affect the number of reproductions and the increase in the number of COVID cases. The results obtained show that the rate of self-isolation at home and the rate of hospitalism have a negative relationship. On the other hand, infections will decrease when the two parameters increase. From the sensitivity of the results, we formulate a control model using optimal control theory by considering two control variables. The result shows that the control strategies minimize the spread of the COVID infection in the population.

Abstract licence: CC BY-NC

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