Introduction
My interest in the spread of infectious diseases sparked after I watched ‘Contagion’, a film that demonstrated the effects of a worldwide epidemic. The speed and severity of the situation of the epidemic in the film really intrigued and encouraged me to delve deeper into the issue of epidemics. At first, I didn’t understand just how mathematics fit in the notion of an epidemic; however, after further research, I realized that the spread of infectious diseases is actually completely based on math itself. In this research paper, I will be investigating and modeling the spread of infectious diseases through the SIR model.
Infectious diseases have made significant impacts on human life across the world. For example, the 1918 Spanish …show more content…
The total population of these three compartments is fixed. The SIR model shows the changes in each compartment. This is done by using rate of change equations, which are explained below.
Rate of change equation for the population changed from the infectious to the recovery compartment:
The rate of change for the recovery group is modeled through the equation:
dR/dt= γI
(Manning)
The infectious compartment will have the disease and be able to transmit it up until a certain number of days, which is calculated using the basic reproductive number, denoted as the R0. The R0 is the number of people that are expected to be infected by one person who has the disease. This number is determined by epidemiological data that is based on a fixed population. Taking the example of measles, those infected can transmit the disease 4 days before the rash shows and 4 days after, so 8 days in total (Facts about Measles). Hence, a person just moved into the infectious compartment will have the disease for 8 days, and then will be moved to recovery. The γ here is a fraction of infected members that are expected to recover per day (Manning). Therefore, in this case, γ = 1/8. To find the change from the infectious compartment to the recovery compartment each day, this fraction has to be multiplied by the number of individuals in the infectious …show more content…
However, the change in the compartments is not very clear from only 10 sets of data. Hence, more data can be collected and tabulated using the formulae in order to give a better representation of this
My interest in the spread of infectious diseases sparked after I watched ‘Contagion’, a film that demonstrated the effects of a worldwide epidemic. The speed and severity of the situation of the epidemic in the film really intrigued and encouraged me to delve deeper into the issue of epidemics. At first, I didn’t understand just how mathematics fit in the notion of an epidemic; however, after further research, I realized that the spread of infectious diseases is actually completely based on math itself. In this research paper, I will be investigating and modeling the spread of infectious diseases through the SIR model.
Infectious diseases have made significant impacts on human life across the world. For example, the 1918 Spanish …show more content…
The total population of these three compartments is fixed. The SIR model shows the changes in each compartment. This is done by using rate of change equations, which are explained below.
Rate of change equation for the population changed from the infectious to the recovery compartment:
The rate of change for the recovery group is modeled through the equation:
dR/dt= γI
(Manning)
The infectious compartment will have the disease and be able to transmit it up until a certain number of days, which is calculated using the basic reproductive number, denoted as the R0. The R0 is the number of people that are expected to be infected by one person who has the disease. This number is determined by epidemiological data that is based on a fixed population. Taking the example of measles, those infected can transmit the disease 4 days before the rash shows and 4 days after, so 8 days in total (Facts about Measles). Hence, a person just moved into the infectious compartment will have the disease for 8 days, and then will be moved to recovery. The γ here is a fraction of infected members that are expected to recover per day (Manning). Therefore, in this case, γ = 1/8. To find the change from the infectious compartment to the recovery compartment each day, this fraction has to be multiplied by the number of individuals in the infectious …show more content…
However, the change in the compartments is not very clear from only 10 sets of data. Hence, more data can be collected and tabulated using the formulae in order to give a better representation of this