Hi Abiy,

In a LogPlot the y axis is always logarithmic. You could plot the Log of the function on a linear y scale. e.g.

Plot[Evaluate[Log@{x[t], y[t], z[t]} /. First@soln11], {t, 0, 10}, 
 Frame -> True, PlotLegends -> {"x", "y", "z"}]

Or a linear plot with a specific range / ticks

Plot[Evaluate[{x[t], y[t], z[t]} /. First@soln11], {t, 0, 10},
 PlotRange -> {0, 1.6},
 Frame -> True,
 FrameTicks -> {{Range[0, 1.6, .2], None}, {Automatic, None}},
 PlotLegends -> {"x", "y", "z"}]

Do you mean this? (Note that the first four functions are for eta = 0 )

s = 2.6 10^4;(*cells per ml per day)*)d = 0.0026;(*day^(-1)*)\[Beta] =
  3 10^(-7);(*(Virion per mililiter)^(-1)*)\[Delta] = \
0.5;(*day^(-1)*)c = 5;(*day^(-1)*)p = 100;(*virions per ml per cell \
per day*)\[Eta] = {0.00, 1.00};
\[Epsilon] = {0.80, 0.95, 0.99, 1};
(*Initial Conditions*)
t0 = (c*\[Delta])/(p*\[Beta]); x0 = 2.0*10^(6); v0 = 10^7;

eqn1a[i_, 
  j_] := {T'[t] == s - d*T[t] - (1 - \[Eta][[i]])*\[Beta]*T[t]*V[t], 
  x'[t] == (1 - \[Eta][[i]])*\[Beta]*T[t]*V[t] - \[Delta]*x[t], 
  V'[t] == (1 - \[Epsilon][[j]])*p*x[t] - c*V[t], T[0] == t0, 
  x[0] == x0, V[0] == v0}

soln11[eq_] := NDSolve[eq, {T, x, V}, {t, 0, 14}]

tt = Flatten[Table[eqn1a[i, j], {i, 2}, {j, 4}], 1];
sol = Flatten[soln11 /@ tt];
solv = (V /. #)[t] & /@ Select[sol, MemberQ[#, V] &];

p1 = LogPlot[solv, {t, 0, 14}, PlotRange -> {100, 10^7}, 
  PlotPoints -> 200, Frame -> True, 
  PlotStyle -> Table[If[i <= 4, Thick, Dashed], {i, 8}]]

Hi Hans

I do not understand why the i-loop starts with 2 and j doesn't reach 4.

In WL the role of ; and , is reversed relative to languages like C.

For[i = 1; j = 1, i < 3, j++; i++,
  Print[" i ", i];
  Print[" j ", j]];

As you suggested, Table is a much better option that For.

Try

Table[Which[i == 1 \[Or] i == 3 \[Or] i == 5, {Red, Thin}, 
  i == 2 \[Or] i == 4 \[Or] i == 6, {Green, Thin}, 
  True, {Blue, Thin}], {i, 8}]

Dear Hans Dolhaine, my version is 11 and it has a way of solving stochastic differential equations!! ItoProcess is also known as Ito diffusion or stochastic differential equation (SDE). ItoProcess is a continuous-time and continuous-state random process. If the drift a is an -dimensional vector and the diffusion b an × -dimensional matrix, the process is -dimensional and driven by an -dimensional WienerProcess.

An Ito process is a type of stochastic process described by Japanese mathematician Kiyoshi Itô, which can be written as the sum of the integral of a process over time and of another process over a Brownian motion.

My problem is I keep getting this error, "Thread::tdlen: Objects of unequal length in 1 cannot be combined." This message is generated when a threading operation is used with expressions that do not have the same length. I just am trying to find a way to run it.

But thank you for your help till now.

Dear Hans Dolhaine and Rahul, I need one more favor as always!! I wanted to change the equation (eqn1a) as ItoProcess so that I can change the above equations by adding some stochastic terms. Then instead of NDSolve, I want to use Randomfunction and finally draw the ListLinePlot of solv2. But it seems something is wrong and I cannot get any results. Can you please run the code below and lead me in the right direction??? Thank you!!

s = 2.6 *10^4;
d = 0.0026;
\[Beta] = 3 *10^(-7);
\[Delta] = {0.5, 5};
c = 5;
p = {5, 100};
\[Epsilon] = {0.00, 0.00};
\[Eta] = {0.80, 0.95, 0.99, 1};

\[Eta]a = {0.00, 1.00};
\[Epsilon]a = {0.80, 0.95, 0.99, 1};
(*Initial Conditions*)
t01 = 2.4*10^6;
v01 = 4.0*10^5;
t0 = {(c*\[Delta][[2]])/(p[[2]]*\[Beta]), (c*\[Delta][[1]])/(p[[
       2]]*\[Beta])};
x0 = 2.0*10^(6); v0 = 4.0*10^7;
(* SDES for p=100, delta=0.5 for fig A*)
Subscript[\[Sigma], 1] = 0.07; Subscript[\[Sigma], 2] = 0.5; \
Subscript[\[Sigma], 3] = 3;


s2 = s/d; R2 = 0; p2 = 0;

eqn1a[i_, j_] := 
 ItoProcess[{\[DifferentialD]T[
      t] == (s - 
        d*T[t] - (1 - \[Eta]a[[i]])*\[Beta]*T[t]*
         V[t]) \[DifferentialD]t + 
     Subscript[\[Sigma], 
      1] (x[t] - s2) \[DifferentialD]w1[t], \[DifferentialD]x[
      t] == ((1 - \[Eta]a[[i]])*\[Beta]*T[t]*V[t] - \[Delta][[1]]*
         x[t]) \[DifferentialD]t + 
     Subscript[\[Sigma], 
      2] (y[t] - R2) \[DifferentialD]w2[t], \[DifferentialD]V[
      t] == ((1 - \[Epsilon]a[[j]])*p[[2]]*x[t] - 
        c*V[t]) \[DifferentialD]t + 
     Subscript[\[Sigma], 3] (z[t] - p2) \[DifferentialD]w3[t]}, {x[t],
    y[t], z[t]}, {{x, y, z}, {t0[[2]], x0, v0}}, 
  t, {w1 \[Distributed] WienerProcess[], 
   w2 \[Distributed] WienerProcess[] , 
   w3 \[Distributed] WienerProcess[]}]

soln11[eq_] := 
  RandomFunction[eq, {T, x, V}, {t, 0., 14., 0.0001}, 
   Method -> "Milstein"];
tt2 = Flatten[Table[eqn1a[i, j], {i, 2}, {j, 4}], 1];
sol2 = Flatten[soln11 /@ tt2];
solv2 = (V /. #)[t] & /@ Select[sol2, MemberQ[#, V] &];


p2 = ListLinePlot[Evaluate[solv2], PlotRange -> All, Frame -> True, 
  FrameLabel -> {Days, "Simulated Decrease Log10 HCV"}, 
  PlotStyle -> Table[If[i <= 4, {Red, Thin}, {Blue, Dashed}], {i, 8}]]

Dear Hans Dolhaine, you are right that I needed it at the beginning not to repeat the same code for different plots( dashed(p2) and thick(p3)) using an if loop(which can easily be applied on Matlab). But the if loop were not able to give me the plot I want(had the if loop were working p2 would have been enough to plot all and p3 was not needed). Thus I finally decided to ignore the join as Rohit suggested and plot thick and dashed lines on different codes as below. I honestly thank both of you for being a big help in my Mathematica coding. If possible, help me to keep p2 and p3 in a single code (i=1(j=1:4)thick lines and i=2(j=1:4) dashed lines) using if loop than being redundant and not to use the Show function. Here is the code for both to see and if possible improve. Kind regards. (Thank you again!!)

s = 2.6*10^4;
d = 0.0026;
\[Beta] = 3 *10^(-7);
\[Delta] = {0.5, 5};
c = 5;
p = {5, 100};

\[Epsilon] = {0.00, 0.00};
\[Eta] = {0.80, 0.95, 0.99, 1};

\[Eta]a = {0.00, 1.00};
\[Epsilon]a = {0.80, 0.95, 0.99, 1};
(*Initial Conditions*)
t0 = {(c*\[Delta][[2]])/(p[[2]]*\[Beta]), (c*\[Delta][[1]])/(p[[
       2]]*\[Beta])};
x0 = 2.0*10^(6); v0 = 4.0*10^7;
(* SDES for p=100, delta=0.5 for fig A*)
eqn1a[i_, 
  j_] := {T'[t] == s - d*T[t] - (1 - \[Eta]a[[i]])*\[Beta]*T[t]*V[t], 
  x'[t] == (1 - \[Eta]a[[i]])*\[Beta]*T[t]*V[t] - \[Delta][[1]]*x[t], 
  V'[t] == (1 - \[Epsilon]a[[j]])*p[[2]]*x[t] - c*V[t], 
  T[0] == t0[[2]], x[0] == x0, V[0] == v0}

 soln11[eq_] := NDSolve[eq, {T, x, V}, {t, 0, 14}]

(* Solving the SDES *) 
tt2 = Flatten[Table[eqn1a[i, j], {i, 2}, {j, 4}], 1];
sol2 = Flatten[soln11 /@ tt2];
solv2 = (V /. #)[t] & /@ Select[sol2, MemberQ[#, V] &];

p2 = Plot[Evaluate[Log10@Take[solv2, 4]], {t, 0, 14}, 
   PlotRange -> {2.6, 8}, Frame -> True, 
   FrameLabel -> {Days , "Simulated Decrease Log10 HCV"},
   PlotStyle -> Table[If[i <= 4, {Red, Thin}, {Blue, "--"}], {i, 8}]];
(*Plot B eta=0 *)
p3 = Plot[Evaluate[Log10@Take[solv2, -4]], {t, 0, 14}, 
   PlotRange -> {2.6, 8}, Frame -> True, 
   FrameLabel -> {Days , "Simulated Decrease Log10 HCV"}, 
   PlotStyle -> Table[If[i <= 4, {Blue, Dashed}], {i, 8}]];
(* Draw together*)
p41 = Show[p2, p3]

Hi Abiy,

What is the reason for joining {1, 1, 1, 1} to the list of plots? It is just going to plot a straight line at y = 1. Is this what you are looking for?

p3 = Plot[Evaluate[Log@Take[Solv1 + Solv2, 4]], {t, 0, 14},
  PlotRange -> Log@{100, 10^7},
  PlotPoints -> 200,
  Frame -> True,
  FrameLabel -> {"Time", "copies "}]

I want to have the y-axis ticks at {0,0.2,0.4,0.6,0.8,1, 1.2,1.4, 1.6} instead of in {0,10^(-4), 0.001, 0.01, 0.1,1}. Please see the plot of the code below and help me in improving it by plotting the y-axis in step size of 0.2. Both Ticks and Frame Ticks were not able to help me.

 k = 6.7 *10^-8; c = 
         2*10^6; \[Alpha] = 1.34; \[Lambda] = 3.3; \[Mu] = 2; X = 10^6;
        r = 0.17*10^6;
        S = 0.83 *10^6;
        P = 10^7;
        a = \[Alpha]/(k*c);
         l = \[Lambda]/(k*c);
        m = \[Mu]/(k*c);
        s1 = S/c; R1 = r/c; p1 = P/c;
        b = 15;
    (*Initial Conditions*)

    x0 = 0.3; y0 = 0.2; z0 = 5;

    (*Differential Equations*)

    rhs1[x_, y_, z_] := x (a (1 - (x + y)) - z);
    rhs2[x_, y_, z_] := -l y + x z;
    rhs3[x_, y_, z_] := -z x + b l y - m z;

   detstab := {x'[t] == rhs1[x[t], y[t], z[t]], 
       y'[t] == rhs2[x[t], y[t], z[t]], z'[t] == rhs3[x[t], y[t], z[t]], 
       x[0] == x0, y[0] == y0, z[0] == z0};
    soln11 = NDSolve[detstab, {x, y, z}, {t, 0, 10}];
    LogPlot[Evaluate[{x[t], y[t], z[t]} /. First@soln11], {t, 0, 10}, 
     PlotRange -> {{0, 10}, {0, 1.2}}, 
     Ticks -> {Table[i + 2, {i, 0, 10}], Table[i + 0.2, {i, 0, 1}]}, 
     Frame -> True]

I would like to plot V and VNI together as V+VNI and the code below is not helping. Mr. Hans Dolhaine, May I get the usual help please?

  s = 2.6 10^4;
      d = 0.0026;
      \[Beta] = 2.25 10^(-7);
      \[Delta] = 1;
      c = 6;
      p = 2.9;  
    \[Epsilon] = {0.96, 0.5};
        \[Rho] = {0, 1};
        eqn1g[i_, j_] := {x'[t] == \[Beta] *T*V[t] - \[Delta] *x[t], 
           V'[t] == (1 - \[Rho][[i]]) (1 - \[Epsilon][[j]])*p *x[t] - 
             c *V[t], 
           VNI'[t] == \[Rho][[i]]*(1 - \[Epsilon][[j]])*p *x[t] - c *VNI[t], 
           x[0] == x0, V[0] == v0, VNI[0] == 0};

        soln112[eq_] := NDSolve[eq, {x, V, VNI}, {t, 0, 14}];
        tableway1 = Flatten[Table[eqn1g[i, j], {i, 2}, {j, 2}], 1];
        Solsn1 = Flatten[soln112 /@ tableway];
        Solv1 = (V /. #)[t] & /@ Select[Solsn1, MemberQ[#, V] &];
        Solv2 = (VNI /. #)[t] & /@ Select[Solsn1, MemberQ[#, VNI] &];
        p3 = LogPlot[
          Evaluate[Join[Take[Solv1 + Solv2, 4], {1, 1, 1, 1}]], {t, 0, 14}, 
          PlotRange -> {100, 10^7}, PlotPoints -> 200, Frame -> True, 
          FrameLabel -> {"Time" , "copies "}]

Yes Sir you understood me well, but the above code makes all 8 plots dashed, no thick line (just changed the thick lines of the first code by dashed, I want it to be mixed: first four thick and the rest Dashed).

Thank you Sir!! It seems working.

s = 2.6 10^4;(*cells per ml per day)*)
d = 0.0026;(*day^(-1)*)
\[Beta] = 3 10^(-7);(*(Virion per mililiter)^(-1)*)
\[Delta] = 0.5;(*day^(-1)*)
c = 5;(*day^(-1)*)
p = 100;(*virions per ml per cell per day*)
\[Eta] = {0.00, 1.00};
\[Epsilon] = {0.80, 0.95, 0.99, 1};
eqn1 = {0, 0, 0, 0};
(*Initial Conditions*)
t0 = (c*\[Delta])/(p*\[Beta]); x0 = 2.0*  10^(6); v0 = 10^7;
For[i = 1, j = 1; i < 3, j < 5; j++, i++; 
 eqn1[[i]] := {T'[t] == 
    s - d * T[t] - (1 - \[Eta][[i]])*\[Beta] *T [t]*V[t], 
   x'[t] == (1 - \[Eta][[i]])*\[Beta] *T[t]*V[t] - \[Delta] *x[t], 
   V'[t] == (1 - \[Epsilon][[j]])*p *x[t] - c *V[t], T[0] == t0, 
   x[0] == x0, V[0] == v0}; 
 soln11[[i]] = NDSolve[eqn1[[i]], {T, x, V}, {t, 0, 14}]; 
 p1 = LogPlot[
   Evaluate[{V[t]} /. First@soln11[[i]], {t, 0, 14}, 
    PlotRange -> {100, 10^8}, PlotPoints -> 200, Frame -> True, 
    PlotStyle -> {Orange, Thick}]]