A fractional-order model for computer viruses and some solution associated with residual power series method

Figures & data

Figure 1. Comparison between the RK and RPS solution of $S(t)$.

Table 1. Approximate solution of $S(t)$ using RK4 and RPS methods.

t	$\mathrm{RK}S(t_i),\alpha =1$	$\mathrm{RPS}S(t_i),\alpha =1$	$Ab{s}_S(t_i)$	$Re{l}_S(t_i)$
0	3	3	0	0
0.01	2.77843	2.77843	${3.22464}^{-9}$	${1.1606}^{-9}$
0.02	2.65554	2.65554	${9.27018}^{-10}$	${3.49089}^{-10}$
0.03	2.61433	2.61433	${1.99140}^{-9}$	${7.61725}^{-10}$
0.04	2.64152	2.64152	${1.94573}^{-10}$	${7.36593}^{-11}$
0.05	2.72662	2.72662	${2.26315}^{-10}$	${8.30022}^{-11}$
0.06	2.86124	2.86124	${8.17013}^{-11}$	${2.85545}^{-11}$
0.07	3.03862	3.03862	${5.86511}^{-10}$	${1.93019}^{-10}$
0.08	3.25322	3.25322	${1.84048}^{-8}$	${5.65741}^{-9}$
0.09	3.50048	3.50048	${2.34799}^{-7}$	${6.70762}^{-8}$
0.1	3.77656	3.77656	${2.16865}^{-6}$	${5.74239}^{-7}$

Table 2. Approximate solution of $A(t)$ using RK4 and RPS methods.

t	$\mathrm{RK}A(t_i),\alpha =1$	$\mathrm{RPS}A(t_i),\alpha =1$	$Ab{s}_A(t_i)$	$Re{l}_A(t_i)$
0	1	1	0	0
0.01	1.25592	1.25592	${1.13764}^{-9}$	${9.05819}^{-10}$
0.02	1.54662	1.54662	${3.47133}^{-9}$	${2.24446}^{-9}$
0.03	1.87043	1.87043	${5.33983}^{-9}$	${2.85487}^{-9}$
0.04	2.22465	2.22465	${8.69501}^{-9}$	${3.90849}^{-9}$
0.05	2.60573	2.60573	${1.17096}^{-8}$	${4.49377}^{-9}$
0.06	3.00947	3.00947	${1.51163}^{-8}$	${5.02291}^{-9}$
0.07	3.43118	3.43118	${1.89419}^{-8}$	${5.52053}^{-9}$
0.08	3.86597	3.86597	${2.27410}^{-8}$	${5.88235}^{-9}$
0.09	4.30892	4.30892	${1.74213}^{-8}$	${4.04308}^{-9}$
0.1	4.75527	4.75527	${6.68440}^{-8}$	${1.40568}^{-8}$

Table 3. Approximate solution of $I(t)$ using RK4 and RPS methods.

t	$\mathrm{RK}I(t_i),\alpha =1$	$\mathrm{RPS}I(t_i),\alpha =1$	$Ab{s}_I(t_i)$	$Re{l}_I(t_i)$
0	95	95	0	0
0.01	86.8293	86.8293	${1.71273}^{-9}$	${1.97253}^{-11}$
0.02	79.2936	79.2936	${3.65712}^{-9}$	${4.61212}^{-11}$
0.03	72.3505	72.3505	${4.85059}^{-9}$	${6.7043}^{-11}$
0.04	65.9589	65.9589	${9.42981}^{-9}$	${1.42965}^{-10}$
0.05	60.0801	60.0801	${1.25570}^{-8}$	${2.09005}^{-10}$
0.06	54.6776	54.6776	${1.53807}^{-8}$	${2.81297}^{-10}$
0.07	49.7173	49.7173	${1.61516}^{-8}$	${3.24869}^{-10}$
0.08	45.1675	45.1675	${6.92892}^{-9}$	${1.53405}^{-10}$
0.09	40.9984	40.9984	${2.91477}^{-7}$	${7.10946}^{-9}$
0.1	37.1826	37.1826	${2.88429}^{-6}$	${7.75709}^{-8}$

Table 4. Approximate solution of $R(t)$ using RK4 and RPS methods.

t	$\mathrm{RK}I(t_i),\alpha =1$	$\mathrm{RPS}I(t_i),\alpha =1$	$Ab{s}_I(t_i)$	$Re{l}_I(t_i)$
0	1	1	0	0
0.01	9.13632	9.13632	${2.64954}^{-9}$	${2.90001}^{-10}$
0.02	16.5042	16.5042	${7.41228}^{-10}$	${4.49115}^{-11}$
0.03	23.1648	23.1648	${2.48064}^{-9}$	${1.07087}^{-10}$
0.04	29.1749	29.1749	${9.29361}^{-10}$	${3.18548}^{-11}$
0.05	34.5875	34.5875	${1.07384}^{-9}$	${3.10469}^{-11}$
0.06	39.4517	39.4517	${1.82688}^{-10}$	${4.63067}^{-12}$
0.07	43.8129	43.8129	${2.20384}^{-9}$	${5.03012}^{-11}$
0.08	47.7133	47.7133	${1.12651}^{-8}$	${2.361}^{-10}$
0.09	51.1922	51.1922	${7.40994}^{-8}$	${1.44747}^{-9}$
0.1	54.2856	54.2856	${6.48794}^{-7}$	${1.19515}^{-8}$

Figure 2. Comparison between the RK and RPS solution of $A(t)$.

Figure 3. Comparison between the RK and RPS solution of $I(t)$.

Figure 4. Comparison between the RK and RPS solution of $R(t)$.

Figure 5. The RPS solution of $S(t)$ for different values of α.

Figure 6. The RPS solution of $A(t)$ for different values of α.

Figure 7. The RPS solution of $I(t)$ for different values of α.

Figure 8. The RPS solution of $R(t)$ for different values of α.