In our case we categorize the individuals into eight states and label them as follows: human infected with bubonic plague (type 1), human infected with septicemic plague (type 2), human infected with pneumonic plague (type 3), rodent infected with bubonic plague (type 4), rodent infected with septicemic plague (type 5), rodent infected with pneumonic plague (type 6), flea infested with pathogens (type 7), and the pathogens in the environment (type 8).
We assume and label individual with bubonic plague as stage one of the disease, septicemic plague as stage two, and pneumonic plague as stage three.
For example, humans with bubonic plague [I.sub.HB] (type at infection 1) do not produce type at infections 1 (human infected with bubonic plague), 4 (rodent infected with bubonic plague), 5 (rodent infected with septicemic plague), 6 (rodent infected with pneumonic plague), and 8 (pathogens in the environment).
Septicemic plague in human may be produced in various ways: progression of untreated human with bubonic plague to human with septicemic plague, adequate contact (including sexual contact) between humans with septicemic plague, adequate contact between rodent and human with septicemic plague, and being acquired from the flea infested with pathogens.
The septicemic plague in rodent is produced in three ways; the first way is when infected rodent with bubonic plague progresses and becomes septicemic plague infective agent at the rate [[gamma].sub.3] (1-[phi]).
Fleas are infested with pathogens from humans and rodents infected with bubonic and septicemic plague at the average rates [bar.[[gamma].sub.hbf]], [bar.[[gamma].sub.hsf]], [bar.[[gamma].sub.rbf]], and [bar.[[gamma].sub.rsf]].
Figures 2 and 1 show how the progression rates from individuals with bubonic plague to individuals with septicemic plague affect the average number of secondary infections in human beings and rodents, respectively.
Results in Figures 3 and 4 show the effect of infection from infectious flea to human beings with bubonic and septicemic plague on the average number of secondary infections.
This result is in light of the fact that the reduction of flea population will reduce the number of individuals with bubonic and septicemic plague and as a result reduce the number of pneumonic plague infective agents that result from the progression of individual with bubonic and septicemic plague.
The number of fleas getting the disease increases with the increase of the rate at which fleas acquire infection from infectious human beings with bubonic plague (see Figure 8(a)) and those with septicemic plague (see Figure 9(a)).
Physical contact that includes sexual contact between two infectious individuals (human beings and rodents) may lead to septicemic plague. The increase in the number of individuals with septicemic plague affects the general dynamics of plague disease, particularly the average number of secondary infections.