Solving Diff. Equation of Epidemic Model: Help Needed

In summary, the conversation is about understanding an article on epidemic deterministic models and a specific equation for compartmental models. The conversation discusses different ways to solve the equation and how to interpret the solutions. It is concluded that there are similarities between the solution provided in the article and the one obtained through the conversation.
  • #1
madiha.sahar
2
0
I am trying to understand this article at Wikipedia on epidemic deterministic models
http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

it is said that if
ds/dt = -b*s(t)*i(t) is divided by dr/dt= ki(t) and is integrated by using chain rule, the answer is S(t) = S(0)exp (-Ro(Rinf - R(0))

but if i solve it, answer i get is r = 1/Ro * lns + c

i have no clue how can i get this answer.

Can anyone help me understand this please.
 
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  • #2


Your solution may well be the inverse of the wiki solution. Ignoring the constant, if s = S(0)exp(-Ro(R - R(0)) then
ln s = ln S0 - Ro r, where r = R - R0.
ln s - ln S0 = -Ro r.
r = -ln(s/S0)/Ro plus a constant. If you normalize to S0 = 1 then r = -ln(s)/Ro + constant. I haven't solved the D.E. but I realized there is a similarity between wiki's and your solution.
 
Last edited:
  • #3


I got it :) thanks a bunch!
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is commonly used to model dynamic systems and predict how they will change over time.

2. How does an epidemic model use differential equations?

An epidemic model uses a system of differential equations to describe the spread of a disease through a population. These equations take into account factors such as the rate of infection and recovery, as well as the size and structure of the population.

3. What is the purpose of solving a differential equation in an epidemic model?

The purpose of solving a differential equation in an epidemic model is to predict the behavior of the disease and its impact on the population. By solving the equations, we can determine how quickly the disease will spread and how many people will be affected.

4. Can differential equations accurately predict the outcome of an epidemic?

While differential equations provide a mathematical framework for modeling epidemics, they may not always accurately predict the outcome. This is because they rely on certain assumptions and simplifications, and real-world epidemics can be influenced by many unpredictable factors.

5. How can I solve differential equations for an epidemic model?

There are various methods for solving differential equations, including analytical solutions and numerical approximations. In an epidemic model, numerical methods are often used due to the complex nature of the equations. These methods involve using computers to simulate the behavior of the system over time.

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