TRANSDUCTION MODEL: COMPARISON BETWEEN SINGLE GENE AND DOUBLE GENE SYSTEM.

By Amogh and Ved

This is the flowchart for the transduction model:

ref:Volkova et al.

Converting this flowchart into system of ODEs we get:

\begin{align}
\frac{dNnewi(t)}{dt} =& pr_{inf} \cdot k \cdot \left( 1 - \frac{Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v}}{Nmax} \right) \cdot \left( Nsus1 + Nsus2 \right) - \frac{1}{t_{newi}} \cdot Nnewi - d \cdot Nnewi - gamma \cdot Nnewi \
\frac{dNsus1(t)}{dt} =& \left( 1 - pr_{inf} \right) \cdot k \cdot \left( 1 - \frac{Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v}}{Nmax} \right) \cdot Nsus1 + \frac{1}{t_{prtp}} \cdot Nprtp - d \cdot Nsus1 - gamma \cdot Nsus1 + \frac{1}{t_{newi}} \cdot Nnewi \cdot \left( 1 - ph_{fr_tp} \right) \cdot b_{fr_inf_lys} \cdot \left( 1 - b_{fr_limm} \right) + gamma \cdot \left( 1 - b_{fr_lys_in} \cdot b_{fr_limm} \right) \cdot \left( Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v} \right) \
\frac{dNsus2(t)}{dt} =& \left( 1 - pr_{inf} \right) \cdot k \cdot \left( 1 - \frac{Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v}}{Nmax} \right) \cdot Nsus2 + \frac{1}{t_{prtp}} \cdot Nprtp - d \cdot Nsus2 - gamma \cdot Nsus2 + \frac{1}{t_{newi}} \cdot Nnewi \cdot \left( 1 - ph_{fr_tp} \right) \cdot b_{fr_inf_lys} \cdot \left( 1 - b_{fr_limm} \right) + gamma \cdot \left( 1 - b_{fr_lys_in} \cdot b_{fr_limm} \right) \cdot \left( Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v} \right) \
\frac{dNlys(t)}{dt} =& k \cdot \left( 1 - \frac{Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v}}{Nmax} \right) \cdot Nlys + \frac{1}{t_{newi}} \cdot Nnewi \cdot \left( 1 - ph_{fr_tp} \right) \cdot b_{fr_inf_lys} \cdot b_{fr_limm} + gamma \cdot b_{fr_lys_in} \cdot b_{fr_limm} \cdot \left( Nsus1 + Nsus2 + Nnewi + Nprtp + Nlys + Nlyt_{t} + Nlyt_{v} \right) - d \cdot Nlys - gamma \cdot Nlys \
\frac{dNprtp(t)}{dt} =& \frac{1}{t_{newi}} \cdot Nnewi \cdot ph_{fr_tp} - \frac{1}{t_{prtp}} \cdot Nprtp - d \cdot Nprtp - gamma \cdot Nprtp \
\frac{dNlyt_{v}(t)}{dt} =& \frac{1}{t_{newi}} \cdot Nnewi \cdot \left( 1 - ph_{fr_tp} \right) \cdot \left( 1 - b_{fr_inf_lys} \right) - \frac{1}{t_{lscl}} \cdot Nlyt_{v} - d \cdot Nlyt_{v} - gamma \cdot Nlyt_{v} \
\frac{dNlyt_{t}(t)}{dt} =& \frac{1}{t_{lscl}} \cdot Nlys - \frac{1}{t_{ltcl_t}} \cdot Nlyt_{t} - d \cdot Nlyt_{t} - gamma \cdot Nlyt_{t} \
\frac{dph_{cir_n}(t)}{dt} =& ph_{br_n} \cdot \left( \frac{1}{t_{lscl}} \cdot Nlyt_{v} + \frac{1}{t_{ltcl_t}} \cdot Nlyt_{t} \right) - Nnewi - ph_{d} \cdot ph_{cir_n} - gamma \cdot ph_{cir_n}
\end{align}