# Démonstrations de R et de RStudio

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‘“$$A = \pi*r^{2}$$”’    $$A = \pi*r^{2}$$

$E = mc^{2}$’    $E = mc^{2}$

### Dates1

‘format(Sys.Date(), “%B %d, %Y”)’    ‘avril 09, 2020’

‘format(Sys.Date(), “%Y-%B-%d”)’    ‘2020-avril-09’

‘format(Sys.Date(), “%Y-%m-%d”)’    ‘2020-04-09’

‘format(Sys.Date(), “%y-%m-%d”)’    ‘20-04-09’

### Statistiques simples avec R

summary((0:9)^2)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
##    0.00    5.25   20.50   28.50   45.75   81.00

### Graphes simples avec R

# Define cars vector with 5 values
cars <- c(1, 3, 6, 4, 9)

# Define some colors ideal for black & white print
colors <- c("white","grey70","grey90","grey50","black")

# Calculate the percentage for each day, rounded to one
# decimal place
car_labels <- round(cars/sum(cars) * 100, 1)

# Concatenate a '%' char after each value
car_labels <- paste(car_labels, "%", sep="")

# Create a pie chart with defined heading and custom colors
# and labels
pie(cars, main="Cars", col=colors, labels=car_labels,
cex=0.8)

# Create a legend at the right
legend(1.5, 0.5, c("Mon","Tue","Wed","Thu","Fri"), cex=0.8,
fill=colors) # Get a random log-normal distribution
r <- rlnorm(1000)

# Get the distribution without plotting it using tighter breaks
h <- hist(r, plot=F, breaks=c(seq(0,max(r)+1, .1)))

# Plot the distribution using log scale on both axes, and use
# blue points
plot(h$counts, log="xy", pch=20, col="blue", main="Log-normal distribution", xlab="Value", ylab="Frequency") ## Warning in xy.coords(x, y, xlabel, ylabel, log): 134 y values <= 0 omitted from ## logarithmic plot ### Tableau des lettres grecques en $$\LaTeX$$ 2 For those of you who don’t know your Greek alphabet, it’s time to learn it : name symbol $$\LaTeX$$ Prononciation et lettre Prononciation et lettre Prononciation et lettre Prononciation et lettre alpha $$\alpha \ A$$ A beta $$\beta \ B$$ B gamma $$\gamma \ \Gamma$$ delta $$\delta \ \Delta$$ epsilon $$\epsilon \ E$$ E (epsilon) $$\varepsilon \ E$$ zeta $$\zeta \ Z$$ Z eta $$\eta \ H$$ theta $$\theta \ \Theta$$ iota $$\iota \ I$$ I kappa $$\kappa \ K$$ K lambda $$\lambda \ \Lambda$$ mu $$\mu \ M$$ M nu $$\nu \ N$$ N xi $$\xi \ \Xi$$ omicron $$\omicron \ O$$ O pi $$\pi \ \Pi$$ rho $$\rho \ P$$ P sigma $$\sigma \ \Sigma$$ tau $$\tau \ T$$ upsilon $$\upsilon \ Y$$ Y phi $$\phi \ \Phi$$ (phi) $$\varphi$$ chi $$\chi \ X$$ X psi $$\psi \ \Psi$$ omega $$\omega \ \Omega$$ - - ### Quelques examples d’utilisation de $$\LaTeX$$ dans des documents R R Markdown allows you to mix text, R code, R output, R graphics, and mathematics in a single document. The mathematics is done using a version of $$\LaTeX$$, the premiere mathematics typesetting program. (Our textbook was done entirely in $$\LaTeX$$. Getting in and out of $$\LaTeX$$ mode You enter $$\LaTeX$$ mode using$latex (for inline mathematics) or $latex (for displayed equations). You get back out of $$\LaTeX$$ mode using either  or$. Some basic mathematics you might use

Commands in $$\LaTeX$$ are preceded by a backslash (). The simplest commands simply produce a symbol: Command Result A B $$\quad$$ $$A \cup B$$ A B $$A \cap B$$ x A $$x \in A$$ 5 2 $$5 \pm 2$$ (x) $$\log(x)$$ (x) $$\sin(x)$$

Other commands take additional inputs (placed inside curly braces {}): Command Result $$\sqrt{27}$$ $$\overline{x}$$ $$\frac{x}{n}$$ $$\binom{k}{n}$$ $$\quad$$ $$\frac{\partial f}{\partial x}$$

The underscore () and carrot (^) have special uses in $$\LaTeX$$. (Note the use of to get inline mathematics set with larger fonts and more vertical space.) Command Result x^2 $$x^2$$ x_2 $$x_2$$ {x} $$\lim_{x \to \infty}$$ _{x} $$\displaystyle \lim_{x \to \infty}$$ _0^{} f(x) ; dx $$\int_0^{\infty} f(x) \; dx$$ _0^{} f(x) ; dx $$\quad$$ $$\displaystyle \int_0^{\infty} f(x) \; dx$$

### Modèles d’épidémies avec R [“Modèle SIR”(https://cran.r-project.org/web/packages/EpiModel/EpiModel.pdf)]

#### Exemple : Modèle SIR Model avec une dynamique vitale (Un Groupe)

param <- param.dcm(inf.prob = 0.2, act.rate = 5,
rec.rate = 1/3, a.rate = 1/90, ds.rate = 1/100,
di.rate = 1/35, dr.rate = 1/100)
init <- init.dcm(s.num = 500, i.num = 1, r.num = 0)
control <- control.dcm(type = "SIR", nsteps = 500)
mod2 <- dcm(param, init, control)
mod2
plot(mod2)