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Model Mathematics

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Component: environment

Component: uninfected_CD4

\frac{d}{d time} (T) = (s_V - (mu_T T)) + r T (1 - (\frac{T + T_1}{T_max})) - (k_1 V T) - (k_1_V_T) s_V = \frac{s_0 theta}{theta + V}

Component: latently_infected_CD4

\frac{d}{d time} (T_1) = k_1 V T + k_1_V_T - (mu_T T_1) - (k_2 T_1)

Component: actively_infected_CD4

\frac{d}{d time} (T_2) = k_2 T_1 - (k_1D D T_2) - (mu_b T_2)

Component: actively_coinfected_CD4

\frac{d}{d time} (T_D2) = k_1D D T_2 - (k_s T_D2) - (mu_bD T_D2)

Component: stably_coinfected_CD4

\frac{d}{d time} (T_D1) = k_s T_D2 - (mu_TD T_D1)

Component: DIV

D = \{\begin{matrix} 0 if time < t_DIV \\ D_ode otherwise \end{matrix} \frac{d}{d time} (D_ode) = \{\begin{matrix} \frac{D_0}{t_DIV} if time < t_DIV \\ N_D_t mu_bD T_D2 + pi_D_t T_D1 - (mu_D D_ode) otherwise \end{matrix} N_D_t = 0.2 N_t pi_D_t = 0.5 mu_b N_t

Component: HIV1

\frac{d}{d time} (V) = N_t mu_b T_2 + N_2_t mu_bD T_D2 - (k_1 V T) - (mu_V V) N_2_t = 0.1 N_t

Component: hybrid_HIV1

\frac{d}{d time} (V_) = N_t_mu_bD T_D2 + pi_t_T_D1 - (mu_V V_) - (k_1_T V_) N_t_= 0.1 N_t pi_t_= 0.01 mu_b N_t

Component: production_function

N_t = N_0 (1 + gamma \frac{{time}^{2}}{{time}^{2} + {t_c}^{2}})

Component: cell_population

T_tot = T + T_1 + T_2 + T_D2 + T_D1

Source: Derived from workspace Nelson, Perelson 1995 at changeset 837457a7e189.

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