Vektor yang ditambahkan dalam penelitian ini adalah kelelawar. Di sarankan untuk penelitian selanjutnya menggunakan vektor lain (seperti lingkungan) yang dapat menjadi penyebab penyebaran penyakit Ebola.
REFERENSI
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[Diakses pada tanggal 4 Januari 2021]
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[12] Centre for Health Protection, Ebola Virus Disease. Tersedia pada https://www.chp.gov.hk/en/healthtopics/content/24/34397.html. [Diakses pada tanggal 3 November 2020]
[13] World Health Organization, Frequently asked
questions on Ebola virus disease. Tersedia pada https://www.who.int/emergencies/diseases/ebola/frequently-asked-questions.
[Diakses pada tanggal 3 November 2020]
[14] H. Anton dan C. Rorres, Elementary Linear Algebra 8th Edition, Jakarta, 2004.
[15] S. L. Ross, Introduction to Ordinary Differential Equations, 4th ed. New Jersey: Wiley, 1989.
[16] W. E. Boyce, R. C. DiPrima, dan D.B. Meade, Elementary Differential Equations and Boundary Value Problems, 11th ed. New Jersey: Wiley, 2017.
[17] M. Manaqib, I. Fauziah, dan Mujiyanti., ”Mathematical Model for Mers-CoV Disease Transmission with Medical Mask Usage and Vaccination”, Indonesian Journal of Pure and Applied Mathematics, vol. 1, no. 2, pp.
97-109, 2019.
[18] G. J. Olsder dan J. W. van der Woude, Mathematical Systems Theory, 2nd ed.
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[19] L. Perko, Differential Equations and Dynamical Systems 3rd Edition Vol. 7, New York: Springer, 2000.
[20] O. Diekmann, J. A. P. Heesterbeek, dan J. A. J. Metz, ”On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations”, Journal of Mathematical Biology, 28, pp. 365–382, 1990.
[21] M. Martcheva, An Introduction to Mathematical Epidemology, New York:
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[22] P. van den Driessche dan J. Watmough, ”Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission”, Mathematical Biosciences vol. 180, pp. 29-48, 2002.
[23] O. Diekmann, J. A. P. Heesterbeek, dan M. G. Roberts, ”The construction of next-generation matrices for compatemental epidemic models”, J. R. Soc.
Interfacevol. 7, pp. 873-885, 2010.
[24] T. Berge, J. Lubuma, A. J. O. Tasse, dan H. M. Tenkam., ”Dynamics of host-reservoir transmission of Ebola with spillover potential to humans”, Electronic Journal of Qualitative Theory of Differential Equations, no. 14, pp. 1-32, 2018.
[25] M. O. Durojaye dan I. J. Ajie., ”Mathematical model of the spread and control of ebola virus disease”, Applied Mathematics, vol. 7 no. 2, pp. 23 - 21, 2017.
[26] Statista, Key epidemiological information on the Ebola virus disease as of 2014 (in days). Tersedia pada
https://www.statista.com/statistics/328946/transmission-parameters-associated-with-ebola/.
[Diakses 16 Januari 2021].
[27] C. M. Rivers, E. T. Lofgren, M. Marathe, S. Eubank, dan B. L. Lewis.,
”Modeling the Impact of Interventions on an Epidemic of Ebola in Sierra
[28] J. Buceta dan K. Johnson., ”Modeling the Ebola zoonotic dynamics: Interplay between enviroclimatic factors and bat ecology”, PLoS ONE, 12(6), pp. 1-14, 2017.
[29] R. Swanepoel, P. A. Leman, F. J. Burt, N. A. Zachariades, L. E. O. Braack, T. G. Ksiazek, P. E. Rollin, S. R. Zaki, dan C. J. Peters., ”Experimental Inoculation of Plants and Animals with Ebola Virus”, Emerging Infectious Diseases, vol. 2, no. 4, 1996.
LAMPIRAN A
PROGRAM MAPLE UNTUK GAMBAR 4.1
>restart;
>with(plots); with(linalg); with(DEtools);
> N[h] := 491794; N[v] := 10864; mu[h] := 0.03; mu[v] := 0.0027; beta[h] :=
0.0473; beta[q] := 0.0016; beta[s] := 0.2; b := 0.001; c := 0.16; u := 0.5; tau :=
b*N[v]; delta[h] := 0.1428; local(gamma[h]); 1; gamma[h] := 0.102; delta[v] :=
0.04762;
>ds[h] := -c*ih*sh*beta[s] - iv*sh*tau*beta[h] - sh*mu[h] + mu[h];
>de[h] := c*ih*sh*beta[s] + iv*sh*tau*beta[h] - eh*delta[h] - eh*mu[h];
>di[h] := eh*delta[h] - ih*gamma[h] - ih*mu[h];
>ds[v] := -iv*sv*u*beta[q] - sv*mu[v] + mu[v];
>de[v] := iv*sv*u*beta[q] - ev*delta[v] - ev*mu[v];
>di[v] := ev*delta[v] - iv*mu[v];
>j := beta[q]*u*delta[v]; x := mu[v]2; y := mu[v]*delta[v]; R0 := j/(x + y);
> f := beta[s]*c*delta[h]; g := mu[h] + delta[h]; k := mu[h] + gamma[h]; R1 :=
f/(g*k);
>de1 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[h]));
>de2 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(de[h]));
>de3 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(di[h]));
>de4 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[v]));
>de5 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv =
i[v](t), eval(di[v]));
>sa := e[h](0) = 0.1, e[v](0) = 0.3, i[h](0) = 0.3, i[v](0) = 0.3, s[h](0) = 0.3, s[v](0)
= 0.4 >sistem := diff(e[h](t), t) = de2, diff(e[v](t), t) = de5, diff(i[h](t), t) = de3, diff(i[v](t), t) = de6, diff(s[h](t), t) = de1, diff(s[v](t), t) = de4;
>z := dsolve(sistem union sa, e[h](t), e[v](t), i[h](t), i[v](t), s[h](t), s[v](t), type = numeric, output = listprocedure, range = 0 .. 50);
> plot([subs(z, s[h](t)), subs(z, e[h](t)), subs(z, i[h](t)), subs(z, s[v](t)), subs(z, e[v](t)), subs(z, i[v](t))], 0 .. 500, linestyle = [solid, dot, dash, longdash, spacedash, dash], legend = [”s[h]”, ”e[h]”, ”i[h]”, ”s[v]”, ”e[v]”, ”i[v]”], legendstyle = [font = [”roman”, 12], location = bottom], labels = [”t(hari)”, ”kompartemen”], labelfont
= [”roman”, 10]);
LAMPIRAN B
PROGRAM MAPLE UNTUK GAMBAR 4.2
>restart;
>with(plots); with(linalg); with(DEtools);
> N[h] := 491794; N[v] := 10864; mu[h] := 0.03; mu[v] := 0.0027; beta[h] :=
0.0473; beta[q] := 0.0016; beta[s] := 0.2; b := 0.001; c := 0.16; u := 0.5; tau :=
b*N[v]; delta[h] := 0.1428; local(gamma[h]); 1; gamma[h] := 0.102; delta[v] :=
0.04762;
>ds[h] := -c*ih*sh*beta[s] - iv*sh*tau*beta[h] - sh*mu[h] + mu[h];
>de[h] := c*ih*sh*beta[s] + iv*sh*tau*beta[h] - eh*delta[h] - eh*mu[h];
>di[h] := eh*delta[h] - ih*gamma[h] - ih*mu[h];
>ds[v] := -iv*sv*u*beta[q] - sv*mu[v] + mu[v];
>de[v] := iv*sv*u*beta[q] - ev*delta[v] - ev*mu[v];
>di[v] := ev*delta[v] - iv*mu[v];
>j := beta[q]*u*delta[v]; x := mu[v]2; y := mu[v]*delta[v]; R0 := j/(x + y);
> f := beta[s]*c*delta[h]; g := mu[h] + delta[h]; k := mu[h] + gamma[h]; R1 :=
f/(g*k);
>de1 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[h]));
>de2 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(de[h]));
>de3 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(di[h]));
>de4 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[v]));
>de5 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv =
i[v](t), eval(di[v]));
>sa := e[h](0) = 0.1, e[v](0) = 0.3, i[h](0) = 0.3, i[v](0) = 0.3, s[h](0) = 0.3, s[v](0)
= 0.4 >sistem := diff(e[h](t), t) = de2, diff(e[v](t), t) = de5, diff(i[h](t), t) = de3, diff(i[v](t), t) = de6, diff(s[h](t), t) = de1, diff(s[v](t), t) = de4;
>z := dsolve(sistem union sa, e[h](t), e[v](t), i[h](t), i[v](t), s[h](t), s[v](t), type = numeric, output = listprocedure, range = 0 .. 50);
> plot([subs(z, s[h](t)), subs(z, e[h](t)), subs(z, i[h](t)), subs(z, s[v](t)), subs(z, e[v](t)), subs(z, i[v](t))], 0 .. 5000, linestyle = [solid, dot, dash, longdash, spacedash, dash], legend = [”s[h]”, ”e[h]”, ”i[h]”, ”s[v]”, ”e[v]”, ”i[v]”], legendstyle = [font = [”roman”, 12], location = bottom], labels = [”t(hari)”, ”kompartemen”], labelfont
= [”roman”, 10]);
LAMPIRAN C
PROGRAM MAPLE UNTUK GAMBAR 4.3
>restart;
>with(plots); with(linalg); with(DEtools);
> N[h] := 491794; N[v] := 10864; mu[h] := 0.03; mu[v] := 0.00027; beta[h] :=
0.0473; beta[q] := 0.0016; beta[s] := 0.8; b := 0.001; c := 0.6; u := 0.5; tau :=
b*N[v]; delta[h] := 0.1428; local(gamma[h]); 1; gamma[h] := 0.102; delta[v] :=
0.04762;
>ds[h] := -c*ih*sh*beta[s] - iv*sh*tau*beta[h] - sh*mu[h] + mu[h];
>de[h] := c*ih*sh*beta[s] + iv*sh*tau*beta[h] - eh*delta[h] - eh*mu[h];
>di[h] := eh*delta[h] - ih*gamma[h] - ih*mu[h];
>ds[v] := -iv*sv*u*beta[q] - sv*mu[v] + mu[v];
>de[v] := iv*sv*u*beta[q] - ev*delta[v] - ev*mu[v];
>di[v] := ev*delta[v] - iv*mu[v];
>j := beta[q]*u*delta[v]; x := mu[v]2; y := mu[v]*delta[v]; R0 := j/(x + y);
> f := beta[s]*c*delta[h]; g := mu[h] + delta[h]; k := mu[h] + gamma[h]; R1 :=
f/(g*k);
>de1 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[h]));
>de2 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(de[h]));
>de3 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(di[h]));
>de4 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[v]));
>de5 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv =
i[v](t), eval(di[v]));
>sa := e[h](0) = 0.1, e[v](0) = 0.3, i[h](0) = 0.3, i[v](0) = 0.3, s[h](0) = 0.3, s[v](0)
= 0.4 >sistem := diff(e[h](t), t) = de2, diff(e[v](t), t) = de5, diff(i[h](t), t) = de3, diff(i[v](t), t) = de6, diff(s[h](t), t) = de1, diff(s[v](t), t) = de4;
>z := dsolve(sistem union sa, e[h](t), e[v](t), i[h](t), i[v](t), s[h](t), s[v](t), type = numeric, output = listprocedure, range = 0 .. 50);
> plot([subs(z, s[h](t)), subs(z, e[h](t)), subs(z, i[h](t)), subs(z, s[v](t)), subs(z, e[v](t)), subs(z, i[v](t))], 0 .. 800, linestyle = [solid, dot, dash, longdash, spacedash, dash], legend = [”s[h]”, ”e[h]”, ”i[h]”, ”s[v]”, ”e[v]”, ”i[v]”], legendstyle = [font = [”roman”, 12], location = bottom], labels = [”t(hari)”, ”kompartemen”], labelfont
= [”roman”, 10]);
LAMPIRAN D
PROGRAM MAPLE UNTUK GAMBAR 4.4
>restart;
>with(plots); with(linalg); with(DEtools);
> N[h] := 491794; N[v] := 10864; mu[h] := 0.03; mu[v] := 0.00027; beta[h] :=
0.0473; beta[q] := 0.0016; beta[s] := 0.8; b := 0.001; c := 0.6; u := 0.5; tau :=
b*N[v]; delta[h] := 0.1428; local(gamma[h]); 1; gamma[h] := 0.102; delta[v] :=
0.04762;
>ds[h] := -c*ih*sh*beta[s] - iv*sh*tau*beta[h] - sh*mu[h] + mu[h];
>de[h] := c*ih*sh*beta[s] + iv*sh*tau*beta[h] - eh*delta[h] - eh*mu[h];
>di[h] := eh*delta[h] - ih*gamma[h] - ih*mu[h];
>ds[v] := -iv*sv*u*beta[q] - sv*mu[v] + mu[v];
>de[v] := iv*sv*u*beta[q] - ev*delta[v] - ev*mu[v];
>di[v] := ev*delta[v] - iv*mu[v];
>j := beta[q]*u*delta[v]; x := mu[v]2; y := mu[v]*delta[v]; R0 := j/(x + y);
> f := beta[s]*c*delta[h]; g := mu[h] + delta[h]; k := mu[h] + gamma[h]; R1 :=
f/(g*k);
>de1 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[h]));
>de2 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(de[h]));
>de3 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(di[h]));
>de4 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv = i[v](t), eval(ds[v]));
>de5 := subs(sh = s[h](t), eh = e[h](t), ih = i[h](t), sv = s[v](t), ev = e[v](t), iv =
i[v](t), eval(di[v]));
>sa := e[h](0) = 0.1, e[v](0) = 0.3, i[h](0) = 0.3, i[v](0) = 0.3, s[h](0) = 0.3, s[v](0)
= 0.4 >sistem := diff(e[h](t), t) = de2, diff(e[v](t), t) = de5, diff(i[h](t), t) = de3, diff(i[v](t), t) = de6, diff(s[h](t), t) = de1, diff(s[v](t), t) = de4;
>z := dsolve(sistem union sa, e[h](t), e[v](t), i[h](t), i[v](t), s[h](t), s[v](t), type = numeric, output = listprocedure, range = 0 .. 50);
> plot([subs(z, s[h](t)), subs(z, e[h](t)), subs(z, i[h](t)), subs(z, s[v](t)), subs(z, e[v](t)), subs(z, i[v](t))], 0 .. 11000, linestyle = [solid, dot, dash, longdash, spacedash, dash], legend = [”s[h]”, ”e[h]”, ”i[h]”, ”s[v]”, ”e[v]”, ”i[v]”], legendstyle = [font = [”roman”, 12], location = bottom], labels = [”t(hari)”,
”kompartemen”], labelfont = [”roman”, 10]);