MATLAB simulation codes for Online Game Addiction with Optimal Control
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Themathematicalmodelanalysisofthedynamicsofonlinegamingaddictionwithoptimalcontrolisthemainemphasisofthis work.Weprovedthatthedynamicalsystem’ssolutionisbounded,positiveandexists.Thelinearizationmethod,theCastillo ChavrztheoremandLaSalle’sinvariantprinciplewereusedtoestablishthestabilityofthesystem’stwoequilibriumpoints, whicharetheendemicandonlinegameaddiction-freeequilibriumpoints.Thebasicreproductionnumber(R0)ofthemodel wascalculatedusingtheprincipleofthenext-generationmatrix,andthesensitivityindicesofR0 tothemodelparameters wereinvestigated.Additionally,bifurcationanalysiswasperformedtoverifythebackwardandforwardbifurcations,andfrom theanalysis,weobservedthatthemodelsystemexhibitsforwardbifurcationatR0=1.Theoptimalcontrolproblemofthe modelwasanalyzedusingPontryagin’smaximumprinciple,andthecharacterizationoftheoptimalcontrolwasconstructed. Numericalsimulationswereperformedtoenhancetheaccuracyoftheanalyticalresults.Thenumericalsimulationofsensitivityanalysis,decreasingthecontactratewithaddicted(β1)andincompletelyrecovered(β2)individuals,theaddictionrate(δ),therelapserate(ω)andtheincompleterecoveryrateoftreatedindividuals(τ)decreasesthereproductionnumber.Usingoptimal control,thecombinedstrategyofminimizingthecontactratewithaddictedindividualsandtherelapserateofincompletely recoveredindividualsminimizestheexposedandaddictedindividualsaswellastheassociatedcost.
