?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=PEMODELAN+MATEMATIKA+PADA+KASUS+TIGA+PREDATOR+SATU%0D%0A%0D%0APREY+DENGAN+DUA+PREDATOR+TERINFEKSI&rft.creator=Hasna+%2C+Wida+Saifana+%09&rft.subject=510+Matematika&rft.description=Pemodelan+matematika+Predator-Prey+atau+Lotka-Voltera+biasanya+melibatkan+2%0D%0Aspesies+yaitu+satu+jenis+spesies+predator+dan+satu+jenis+spesies+prey.+Namun%0D%0Apenelitian+kali+ini+akan+melibatkan+tiga+jenis+spesies+predator(x%2C+y%2C+z)+dan+satu+jenis%0D%0Aspesies+prey(m).+Dimana+ketiga+jenis+spesies+predator+saling+bersaing+untuk%0D%0Aberburu+makanan+(prey)%2C+dan+terdapat+dua+jenis+spresies+predator+yaitu+predator%0D%0Ajenis+kedua(y)+dan+predator+jenis+ketiga(z)+yang+terjangkit+infeksi+menjadi+predator%0D%0Ajenis+kedua+terinfeksi(i)+dan+predator+jenis+ketiga+terinfeksi(j).+Kedua+spesies%0D%0Apredator+yang+terinfeksi(i%2Cj)+diberikan+perlakuan+treatment+atau+pengobatan.%0D%0APredator(y%2C+z)+yang+sehat+diberikan+perlakuan+vaksinasi+untuk+mengurangi+peluang%0D%0Alebih+banyak+predator(y%2C+z)+yang+terinfeksi.+Keadaan+ini+menghasilkan+sistem%0D%0Apersamaan+nonlinear.+Dengan+Batasan+yang+telah+ditentukan%2C+diperoleh+empat+titik%0D%0Aekulibrium+yaitu+E0+%3D+(0%2C0%2C0%2C0%2C0%2C0)%2CE1+%3D+(0%2C0%2C%0D%0A%CE%B2%0D%0Af3%0D%0A%2C+0%2C0%2C%0D%0Ac3%0D%0Ac2%0D%0A)%2CE2+%3D%0D%0A%0D%0A(%0D%0A%CE%B2%0D%0Af1%0D%0A%2C0%2C0%2C0%2C0%2C%0D%0Aa2%0D%0Aa1%0D%0A)%2C+dan+E3+%3D+(0+%2C%0D%0A%CE%B2%0D%0Af2%0D%0A%2C+0%2C0%2C0%2C%0D%0Ab3%0D%0Ab2%0D%0A).+kestabilan+sistem+dapat+diketahui%0D%0Adengan+mensubstitusikan+titik+ekuilibrium+kedalam+matriks+Jacobian+untuk%0D%0Amendapatkan+nilai+eigen+dari+persamaan+karakteristiknya.%0D%0AKata+Kunci%3A+Pemodelan+Predator-Prey%2C+Lotka-Voltera%2C+Titik+Ekuilibrium%2C%0D%0AEkosistem%0D%0A%0D%0APredator-Prey+or+Lotka-Voltera+mathematical+modeling+usually+involves+2+species%2C%0D%0Anamely+one+type+of+predator+species+and+one+type+of+prey+species.+However%2C+this%0D%0Aresearch+will+involve+three+types+of+predator+species(x%2C+y%2C+z)+and+one+type+of+prey%0D%0Aspecies(m).+Where+the+three+types+of+predator+species+compete+with+each+other+to%0D%0Ahunt+for+food+(prey)%2C+and+there+are+two+types+of+predator+species%2C+namely+the+second%0D%0Atype+of+predator(y)+and+the+third+type+of+predator(z)+that+are+infected+with+infection%0D%0Ainto+the+second+type+of+predator+infected(i)+and+the+third+type+of+predator%0D%0Ainfected(j).+Both+infected+predator+species(i%2Cj)+are+given+treatment.+Healthy%0D%0Apredators(y%2C+z)+are+vaccinated+to+reduce+the+chance+of+more+predators+becoming%0D%0Ainfected.+This+situation+results+in+a+nonlinear+system+of+equations.+With%0D%0Apredetermined+constraints%2C+four+equilibrium+points+are+obtained%2C+namely+E0+%3D%0D%0A(0%2C0%2C0%2C0%2C0%2C0)%2CE1+%3D+(0%2C0%2C%0D%0A%CE%B2%0D%0Af3%0D%0A%2C+0%2C0%2C%0D%0Ac3%0D%0Ac2%0D%0A)%2CE2+%3D+(%0D%0A%CE%B2%0D%0Af1%0D%0A%2C0%2C0%2C0%2C0%2C%0D%0Aa2%0D%0Aa1%0D%0A)%2C+dan%0D%0A%0D%0AE3+%3D+(0+%2C%0D%0A%CE%B2%0D%0Af2%0D%0A%2C+0%2C0%2C0%2C%0D%0Ab3%0D%0Ab2%0D%0A).+The+stability+of+the+system+can+be+known+by+substituting+the%0D%0Aequilibrium+points+into+the+Jacobian+matrix+to+obtain+the+eigenvalues+of+the%0D%0Acharacteristic+equation.%0D%0AKeywords%3A+Predator-Prey+Modeling%2C+Lotka-Voltera%2C+Equilibrium+Point%2C+Ecosystem&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM&rft.date=2024-05-07&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84107%2F1%2F1.%2520ABSTRAK%2520-%2520Hasna%2520Wida%2520Saifana.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84107%2F2%2F2.%2520SKRIPSI%2520FULL-1%2520-%2520Hasna%2520Wida%2520Saifana.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84107%2F3%2F3.%2520SKRIPSI%2520TANPA%2520BAB%2520PEMBAHASAN%2520-%2520Hasna%2520Wida%2520Saifana.pdf&rft.identifier=++Hasna+%2C+Wida+Saifana+++(2024)+PEMODELAN+MATEMATIKA+PADA+KASUS+TIGA+PREDATOR+SATU+PREY+DENGAN+DUA+PREDATOR+TERINFEKSI.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F84107%2F