Infectious Disease Essay Example | Topics and Well Written Essays - 1000 words

Infectious Disease - Essay Example So if the transition happens they move into infectious group. Consequently infectious group is the one that spreads it back to susceptible for certain period of time, which is known as ‘infectious period’ after that period they are a considered to be immune for life if recovered. The following picture depicts a basic SIR model used analyzing an infectious disease Using notation from our SIR model there are some equations that can be formed in order to find answer to my IA question. When modelling SIR models it is very important to identify the independent and dependant variables. As in majority of the mathematical models time ‘t’ is going to be independent variable and it is going to be measured in days. More people are getting infected when there is a contact between infected people and susceptible. In our equations represents number of contacts infective person has each day. If we decided that I represents number of all infected people than represents number for all infected contacts per day. But infected people come in contact only with susceptible ones therefore we need to multiply (susceptible fraction of the population) we get: This expression looks like first differential equation, but in our equation of change in susceptible class is negative. It is negative because people from that class are getting removed into the infected class. In order to represent those equations as a derivation they should be expressed with relation to our dependant and independent variables. In order to represent the rate of change as a derivation every dependant variable such as S, I, R should be represented with relation to time. When talking about infectious disease such function of time as ‘next day’ can be represented as: S(t+t) – S(t). Applying those changes to our equations we get: Following the same principle as we used explaining ‘Equation 1’ next day increase in I can be represented by finding all the cases that can happen tomorrow