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Bilangan kromatik total graf G adalah bilangan bulat terkecil k dimana titik-titik dan sisi-sisi graf G dapat diwarnai dengan k warna sedemikian hingga dua titik yang adjecent dan sisi yang insiden dengan titik-titik tersebut diberikan warna yang berbeda. Dalam paper ini dibahas mengenai pewarnaan total pada Graf Bintang Sierpinski, 𝑆𝑆𝑆𝑆 𝑛𝑛 . Bilangan kromatik untuk pewarnaan total pada Graf 𝑆𝑆𝑆𝑆 𝑛𝑛 adalah 1 untuk 𝑛𝑛 = 1 dan 1 + 3. 2 𝑛𝑛−2 untuk 𝑛𝑛 ≥ 2. Kata Kunci: Graf Bintang Sierpinski, Pewarnaan total, Bilangan Kromatik.

A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin’s maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.

We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin's maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.

A model of HIV/AIDS epidemic in homogenous community is proposed and analyzed the global dynamic. The model is studied to investigate the existence of equilibria and analyze the global stability. The global dynamic is determined by the basic reproduction ratio that is obtained from the next generation matrix of the model. The endemic equilibrium point is globally asymptotically stable when this ratio exceeds unity, while the disease free equilibrium achieves the global stability when the ratio is less than unity. The simulation results are presented to simulate the evolution of population in the long term