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PEMODELAN MATEMATIKA SEIR MODIFIKASI PENYALAHGUNAAN GANJA DENGAN DIFERENSIASI GENDER DI INDONESIA
This study aims to develop an SEIRPMHQ mathematical model to describe the dynamics of cannabis abuse by incorporating gender differences within the population. The model is formulated as a system of nonlinear ordinary differential equations that divides the population into eight compartments: susceptible, exposed, active addicts, and recovered individuals for both male and female subpopulations. The model incorporates social transmission, progression from the exposed stage to active addiction, rehabilitation, relapse, and natural mortality. Mathematical analysis was conducted by establishing the positivity and boundedness of solutions, determining the drug-free and drug-present equilibrium points, analyzing local stability using the Jacobian matrix and the Routh–Hurwitz criterion, and calculating the basic reproduction number using the Next Generation Matrix method. The analytical results indicate that the drug-free equilibrium is locally asymptotically stable when the basic reproduction numbers of both male and female subpopulations are less than one. Numerical calculations produced basic reproduction numbers of R 0m ​ =0.4038 and R 0f ​ =0.1142 under the first scenario, and R 0m ​ =0.7539 and R 0f ​ =0.2283 under the second scenario, indicating that the system converges to a drug-free state. In another scenario, the values R 0m ​ =1.2115 and R 0f ​ =0.4281 were obtained, suggesting that cannabis abuse may persist within the male subpopulation. Numerical simulations using the MATLAB ode45 solver over a 50-year period showed that the proportions of exposed and active-addicted males were consistently higher than those of females. Furthermore, the rehabilitation populations increased gradually and approached stable levels, reaching approximately 0.25 for males and 0.20 for females at the end of the simulation period. These findings indicate that social interaction and rehabilitation play significant roles in shaping the dynamics of cannabis abuse within the population.
FAKULTAS SAINS DAN TEKNOLOGI, UIN SUNAN KALIJAGA YOGYAKARTA
PEMODELAN MATEMATIKA SEIR MODIFIKASI PENYALAHGUNAAN GANJA DENGAN DIFERENSIASI GENDER DI INDONESIA (Text)
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