LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! LaTeX Error: Environment aligned undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Undefined control sequence.
<argument> \text 
                 {d} S
l.175 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.175 }{}
         
! Misplaced alignment tab character &.
<argument> ...} \frac {\text {d} S}{\text {d} t} &
                                                  = \nu (t) - \beta (t) S I ...
l.175 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} I
l.175 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.175 }{}
         
! Misplaced alignment tab character &.
<argument> ...\ \frac {\text {d} I}{\text {d} t} &
                                                  = \beta (t) S I - \gamma I...
l.175 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} R
l.175 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.175 }{}
         
! Misplaced alignment tab character &.
<argument> ...\ \frac {\text {d} R}{\text {d} t} &
                                                  = \gamma I - \mu (t) R \en...
l.175 }{}
         
! LaTeX Error: \begin{list} on input line 166 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment aligned undefined.

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Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  \begin {aligned} \beta _{t} &
                                         = \frac {Z_{t} + Z_{t + 1}}{2 S_{t}...
l.187 }{}
         
! Misplaced alignment tab character &.
<argument> ... + 1}}{2 S_{t} I_{t}} \\ S_{t + 1} &
                                                  = \frac {(1 - \frac {1}{2}...
l.187 }{}
         
! Misplaced alignment tab character &.
<argument> ... {1}{2} \mu _{t + 1}} \\ I_{t + 1} &
                                                  = \frac {(1 - \frac {1}{2}...
l.187 }{}
         
! LaTeX Error: \begin{list} on input line 166 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment aligned undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  \begin {aligned} X_{t} &
                                    \sim X(t) \quad [X = \beta , S, I, \mu ]...
l.195 }{}
         
! Misplaced alignment tab character &.
<argument> ... [X = \beta , S, I, \mu ] \\ Z_{t} &
                                                  \sim \int _{t - 1}^{t} \be...
l.195 }{}
         
! Undefined control sequence.
<argument> ...1}^{t} \beta (s) S(s) I(s) \, \text 
                                                  {d} s \\ B_{t} &\sim \int ...
l.195 }{}
         
! Misplaced alignment tab character &.
<argument> ... S(s) I(s) \, \text {d} s \\ B_{t} &
                                                  \sim \int _{t - 1}^{t} \nu...
l.195 }{}
         
! Undefined control sequence.
<argument> ... \int _{t - 1}^{t} \nu (s) \, \text 
                                                  {d} s \end {aligned} 
l.195 }{}
         
! LaTeX Error: \begin{list} on input line 166 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment aligned undefined.

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Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  \begin {aligned} S_{t + 1}^{(i)} &
                                              = \frac {(1 - \frac {1}{2} \mu...
l.350 }{}
         
! Misplaced alignment tab character &.
<argument> ...\ldots , b - 1] \\ S_{a}^{(i + 1)} &
                                                  = S_{b}^{(i)} \end {aligned} 
l.350 }{}
         
! LaTeX Error: \begin{list} on input line 343 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment aligned undefined.

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Type  H <return>  for immediate help.
 ...                                              
! Undefined control sequence.
<argument> \text 
                 {d} S
l.472 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.472 }{}
         
! Misplaced alignment tab character &.
<argument> ...} \frac {\text {d} S}{\text {d} t} &
                                                  = \nu (t) - \beta (t) S I ...
l.472 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} I
l.472 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.472 }{}
         
! Misplaced alignment tab character &.
<argument> ...\ \frac {\text {d} I}{\text {d} t} &
                                                  = \beta (t) S I - \gamma I...
l.472 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} R
l.472 }{}
         
! Undefined control sequence.
<argument> \text 
                 {d} t
l.472 }{}
         
! Misplaced alignment tab character &.
<argument> ...\ \frac {\text {d} R}{\text {d} t} &
                                                  = \gamma I - \mu (t) R \en...
l.472 }{}
         
! LaTeX Error: \begin{list} on input line 463 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment aligned undefined.

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Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  \begin {aligned} B(t) &
                                   = \int _{t - 1}^{t} \nu (s)\,\text {d}s \...
l.481 }{}
         
! Undefined control sequence.
<argument> ...&= \int _{t - 1}^{t} \nu (s)\,\text 
                                                  {d}s \\ Z(t) &= \int _{t -...
l.481 }{}
         
! Misplaced alignment tab character &.
<argument> ...1}^{t} \nu (s)\,\text {d}s \\ Z(t) &
                                                  = \int _{t - 1}^{t} \beta ...
l.481 }{}
         
! Undefined control sequence.
<argument> ...- 1}^{t} \beta (s) S(s) I(s)\,\text 
                                                  {d}s \end {aligned} 
l.481 }{}
         
! LaTeX Error: \begin{list} on input line 463 ended by \end{aligned}.

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Type  H <return>  for immediate help.
 ...