Main Article Content
Abstract
Predator-prey adalah model matematika yang menggambarkan perilaku interaksi dua spesies, satu diantaranya merupakan pemangsa dan satu lainnya sebagai mangsa. Populasi pemangsa biasanya berada di level lebih atas dibandingkan level mangsa pada rantai makanan. Oleh karena itu, populasi pemangsa lebih sedikit dan rentan akan kepunahan baik karena penyakit ataupun kalah persaingan. Pada artikel ini, dikembangkan model predator-prey dengan dua jenis pemangsa dan salah satunya terinfeksi penyakit. Untuk mencegah penyebaran, diberikan tindakan vaksinasi dan pengobatan yang dirumuskan menggunakan Pontryagin Minimum Principle (PMP). Analisis kestabilan dilakukan secara lokal untuk menunjukkan tindakan vaksinasi dan pengobatan berpengaruh terhadap sifat kestabilan. Terakhir, simulasi dilakukan secara numerik guna melihat perilaku model dan performa vaksinasi dan treatment yang diberikan
Article Details
References
- Bate, A. M., Hilker, F.M., Predator– prey oscillations can shift when diseases become endemic, Journal of Theoretical Biology, 316 (2013) pp. 1–8
- Bera, S. P., Maiti, A., Samanta, G.P., A Prey-predator Model with Infection in Both Prey and Predator, Filomat, 29:8 (2015), 1753–1767
- Das, K.P., A mathematical study of a predator-prey dynamics with disease in predator, ISRN Applied mathematics, Vol. 2011 Article ID 807486
- Dash, S.B., Saini, H., Panda T.C., Mishra, A., Predator-Prey Model for Infectious Virtual Machines in IaaS Cloud Environment Based on Lotka-Volterra Equation, Asian Journal of Information Technology, 14(3):84-91, 2015
- Han, L., Ma, Z., Four Predator Prey Models with Infectious Diseases, Mathematical and Computer Modelling, 34 (2001) 849-858, Pergamon
- Hugo, A., Massawe, E.S., Makinde, O.D., An eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population, Journal of Ecology and the Natural Environment, Vol. 4(10), pp. 266-279, July 2012
- Kumar, M., Mishra, B.K., Panda, T.C., Predator-Prey Models on Interaction between Computer Worms, Trojan Horse and Antivirus Software Inside a Computer System, International Journal of Security and Its Applications, Vol. 10, No. 1 (2016), pp.173-190
- Rida, S.Z., Khalil, M., Hosham, H.A., Gadellah, S., predator-prey fractional-order dynamical system with both the populations affected by diseases, Journal of Fractional Calculus and Applications, Vol. 5(3S) No. 13, pp. 1-11
- Shukla, J.B., Singh, G., Shukla, P., Tripathi, A., Modeling and analysis of the effects of antivirus software on an infected computer network, Applied Mathematic and Computation Elsevier, 227(2014):11-18, 2014
- Sooknanan, J., Bhatt, B., Comissiong, D.M.G., A modified predator–prey model for the interaction ofpolice and gangs, R. Soc. Open sci. 3:160083. http://dx.doi.org/10.1098/rsos.160083
References
Bate, A. M., Hilker, F.M., Predator– prey oscillations can shift when diseases become endemic, Journal of Theoretical Biology, 316 (2013) pp. 1–8
Bera, S. P., Maiti, A., Samanta, G.P., A Prey-predator Model with Infection in Both Prey and Predator, Filomat, 29:8 (2015), 1753–1767
Das, K.P., A mathematical study of a predator-prey dynamics with disease in predator, ISRN Applied mathematics, Vol. 2011 Article ID 807486
Dash, S.B., Saini, H., Panda T.C., Mishra, A., Predator-Prey Model for Infectious Virtual Machines in IaaS Cloud Environment Based on Lotka-Volterra Equation, Asian Journal of Information Technology, 14(3):84-91, 2015
Han, L., Ma, Z., Four Predator Prey Models with Infectious Diseases, Mathematical and Computer Modelling, 34 (2001) 849-858, Pergamon
Hugo, A., Massawe, E.S., Makinde, O.D., An eco-epidemiological mathematical model with treatment and disease infection in both prey and predator population, Journal of Ecology and the Natural Environment, Vol. 4(10), pp. 266-279, July 2012
Kumar, M., Mishra, B.K., Panda, T.C., Predator-Prey Models on Interaction between Computer Worms, Trojan Horse and Antivirus Software Inside a Computer System, International Journal of Security and Its Applications, Vol. 10, No. 1 (2016), pp.173-190
Rida, S.Z., Khalil, M., Hosham, H.A., Gadellah, S., predator-prey fractional-order dynamical system with both the populations affected by diseases, Journal of Fractional Calculus and Applications, Vol. 5(3S) No. 13, pp. 1-11
Shukla, J.B., Singh, G., Shukla, P., Tripathi, A., Modeling and analysis of the effects of antivirus software on an infected computer network, Applied Mathematic and Computation Elsevier, 227(2014):11-18, 2014
Sooknanan, J., Bhatt, B., Comissiong, D.M.G., A modified predator–prey model for the interaction ofpolice and gangs, R. Soc. Open sci. 3:160083. http://dx.doi.org/10.1098/rsos.160083