On analysis and optimal control of a SEIRI epidemic model with general incidence rate
Hassan Aghdaoui, Abdesslem Lamrani Alaoui, Kottakkaran Sooppy Nisar, Mouhcine Tilioua
Abstract
This paper deals with the study of a SEIRI epidemic model with relapse and general incidence function. Using the next-generation matrix method, we have looked for the expression of the basic reproduction rate R0 and analyzed the equilibria’s existence and local stability. More precisely, we have established that the two equilibrium points are locally asymptotically stables. In addition, we have used three control functions to control the evolution of the proposed model. We have determined the optimal control by means of the Pontryagin’s maximum principle. Also, some numerical simulations are given to illustrate the theoretical results.
Topics & Concepts
Epidemic modelOptimal controlPontryagin's minimum principleMathematicsApplied mathematicsStability (learning theory)Maximum principleBasic reproduction numberIncidence (geometry)Matrix (chemical analysis)Function (biology)Stability theoryControl (management)Mathematical optimizationControl theory (sociology)Computer sciencePhysicsNonlinear systemBiologyChemistryDemographyGeometryQuantum mechanicsChromatographyMachine learningPopulationSociologyEvolutionary biologyArtificial intelligenceMathematical and Theoretical Epidemiology and Ecology ModelsCOVID-19 epidemiological studiesEvolution and Genetic Dynamics