A delayed HIV infection model with apoptosis and viral loss

Figures & data

Table 1. Descriptions of various parameters.

Parameters	Their descriptions
s	Production rate of uninfected T cells
d	Death rate of uninfected T cells
b	Rate of infection of T cells by virus
${ϵ}_r$	Efficacy of RTI
k	Removal rate of uninfected T cells
B	Bystander apoptosis
δ	Death rate of infected T cells
$d_1$	Rate of action of CTL cells
N	Lysis rate of infected cells
${ϵ}_p$	Efficacy of PI
c	Death rate of virus
η	Loss of virus
p	Production rate of CTL cells
$d_2$	Death rate of CTL cells

Figure 1. Effect of apoptosis.

Table 2. The value of the various parameters.

Parameter	Data 1	Data 2	Data 3
s cells ml day^−1	46	5	200
d day^−1	0.0046	0.3	0.02
b ml viron day^−1	4.8$\times {10}^{-6}$	0.36	0.36
${ϵ}_r$	0.5	0.4	0.5
k cell^−1 day^−1	0.36	0.02	0.1
B day^−1	Varied	350	0.02
δ day^−1	0.1	0.33	0.53
$d_1$ ml viron day^−1	9.4$\times {10}^{-4}$	3.7$\times {10}^{-4}$	8.8
${ϵ}_p$	0.6	0.7	0.6
N virion cell^−1	4000	500	6167
c day^−1	3	3	3
η	20	20	19
p day^−1	0.46	1.4	0.4
$d_2$ day^−1	0.67	0.46	0.41
${\tau }_1$ days	0.09	11.5	0-5
${\tau }_2$ days	2	0.02	10-15

Figure 2. Comparison of single and combination therapy with black line showing single therapy and red line showing combination therapy.

Figure 3. Effect of RTI and PI on the concentration of uninfected T cells (a) density of uninfected T cells for the different efficacy of PI keeping RTI fixed at 0.4, (b) density of uninfected T cells for the different efficacy of PI keeping RTI fixed at 0.4.

Figure 4. Plots showing the asymptotic stability of the infected equilibrium $I_1$ when ${\tau }_1<{\tau }_1^{\ast }$.

Figure 5. Plots showing the occurrence of periodic solutions of the infected equilibrium $I_1$ when${\tau }_1>{\tau }_1^{\ast }$.

Figure 6. Plots showing the asymptotic stability of the infected equilibrium $I_1$ when ${\tau }_2<{\tau }_2^{\ast }$.

Figure 7. Plots showing the occurrence of periodic solutions of the infected equilibrium $I_1$ when${\tau }_2>{\tau }_2^{\ast }$.

Figure 8. Sensitive dependence of solutions on initial conditions.

Figure 9. Bifurcation diagram w.r.t. ${\tau }_1$ and corresponding time series plot.

Figure 10. Bifurcation diagram w.r.t. ${\tau }_2$ and corresponding time series plot.