Solve SIS Disease Model: Help Needed

In summary, the problem discussed is an SIS disease problem, with I(t) representing the number of infectives at time t, N being the total population, b being the infection rate, and v being the recovery rate. The given model for this disease is dI/dt = bI(N-I) - vI, and since the population is assumed constant, S(t) can be taken as N-I(t). The condition for when the number of infectives goes to zero can be derived by solving the separable equation dx=dI \frac{1}{I(bN-v-bI)}, which is a Bernoulli equation.
  • #1
tactical
6
0
The following problem is an SIS disease problem:

Calling: I(t) = number of infectives at time t
N = the total population (assumed constant)
b = infection rate (here, a positive constant)
v = recovery rate (also, a positive constant)

a model for this disease is given bu the following:

dI/dt = bI(N-I) - vI

And since the population is assumed constant, we can just take S(t) to be N -I(t). Derive a condition for when the number of infectives goes to zero.

Is there anyone out there than can help me, even if it's just a little bit?
 
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  • #2
The equation is separable. Just integrate
[tex]dx=dI \frac{1}{I(bN-v-bI)}[/tex]
 
  • #3
it's a Bernoulli equation...I have to solve the same as you...did u solve it?
 
Last edited:

1. What is the SIS disease model?

The SIS disease model is a mathematical model used to study the spread of infectious diseases in a population. It stands for Susceptible-Infected-Susceptible, and it assumes that individuals can become infected, recover, and then become susceptible again.

2. How does the SIS model work?

The SIS model uses a set of differential equations to describe the dynamics of an infectious disease in a population. It takes into account the rates of infection and recovery, as well as the number of susceptible and infected individuals in the population.

3. What is the purpose of solving the SIS model?

Solving the SIS model helps us understand how infectious diseases spread and how interventions, such as vaccinations or social distancing, can impact the spread of the disease. It can also help predict the future course of an outbreak and inform public health strategies.

4. What are the limitations of the SIS model?

The SIS model assumes that individuals can become infected and then recover, but it does not account for other factors such as immunity, age, or geographical location. It also assumes a well-mixed population, which may not always be the case.

5. How can I use the SIS model to help with disease control?

The SIS model can be used to simulate different scenarios and interventions, such as implementing a vaccination program or increasing social distancing measures. By adjusting the parameters in the model, we can determine the most effective strategies for controlling the spread of a disease.

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