mjhjmtu

I am trying to get two rows with two figures in each row using subfigure, but I keep getting errors for this.

documentclass[demo]article % remove 'demo' option in real document
usepackagegraphicx,subcaption
begindocument
beginfigure

beginsubfigure[0.45textwidth]
 includegraphics[width=textwidth]long_pneumonic.jpg
 captionPre-vaccination susceptible and infected 
 population$alpha=0.000015, beta=0.0027, delta=.002, sigma=1/3, 
 Delta=3/4, r=1/5$.
endsubfigure
beginsubfigure0.45textwidth
 includegraphics[width=linewidth]long_pneumonic2.jpg
 captionTransient loops of the infected and susceptible population 
 changes.
endsubfigure
beginsubfigure0.45textwidth
 includegraphics[width=linewidth]long_pneumonic3.jpg
 captionThe population of susceptible individuals and infected 
 individuals over a period of 1500 days post-vaccination.
 $alpha=0.000015, beta=0.0027, delta=.002, sigma=1/3, Delta=3/4, 
 r=1/5$.
endsubfigure
beginsubfigure0.45textwidth
 includegraphics[width=linewidth]long_pneumonic4.jpg
 caption[A graph showing the rise and decrease of pneumonic plague 
 victims leading to increasing amounts of infected with each recurrence 
 post-vaccination.
endsubfigure
captionGraphs comparing and contrasting the same parameters examining the 
dynamics of the susceptible and infected populations pre and post 
vaccinations.
endfigure
enddocument

You wrote,

I keep getting errors

You didn't mention which errors you are getting, but I can only assume that they are caused by the line

beginsubfigure[0.45textwidth]

at the start of the first subfigure environment. Change this line to

beginsubfigure0.45textwidth

i.e., replace the square brackets with curly braces, and the immediate problem should be fixed. (Note that the other three beginsubfigure0.45textwidth directives are already correct.) By the way, I'm assuming that your documents loads the subcaption package, not the obsolete and deprecated subfigure package.

In addition to fixing the syntax error, you may also want to "spruce up" the appearance of the figure. E.g., increase the horizontal separation between the subfigures, increase the space between the two rows of subfigures, and switch from full justification to centering for the captions of the four subfigures.

documentclass[demo]article % remove 'demo' option in real document
usepackagegraphicx,subcaption,ragged2e
begindocument

beginfigure
captionsetup[subfigure]justification=Centering

beginsubfigure[t]0.45textwidth
 includegraphics[width=textwidth]long_pneumonic.jpg
 captionPre-vaccination susceptible and infected population. $alpha=0.000015$, $beta=0.0027$, $delta= 0.002$, $sigma=1/3$, $Delta=3/4$, $r=1/5$.
endsubfigurehspacefill % maximize horizontal separation
beginsubfigure[t]0.45textwidth
 includegraphics[width=linewidth]long_pneumonic2.jpg
 captionTransient loops of the infected and susceptible population changes.
endsubfigure

bigskip % more vertical separation
beginsubfigure[t]0.45textwidth
 includegraphics[width=linewidth]long_pneumonic3.jpg
 captionThe population of susceptible individuals and infected individuals over a period of 1500 days post-vaccination.
 $alpha=0.000015$, $beta=0.0027$, $delta=0.002$, $sigma=1/3$, $Delta=3/4$, 
 $r=1/5$.
endsubfigurehspacefill % maximize horizontal separation
beginsubfigure[t]0.45textwidth
 includegraphics[width=linewidth]long_pneumonic4.jpg
 captionA graph showing the rise and decrease of pneumonic plague victims leading to increasing amounts of infected with each recurrence post-vaccination.
endsubfigure

captionGraphs comparing and contrasting the same parameters examining the dynamics of the susceptible and infected populations pre and post vaccinations.

endfigure
enddocument