# On a general stochastic differential equation for SIS epidemic models

@article{Bernardi2020OnAG, title={On a general stochastic differential equation for SIS epidemic models}, author={Enrico Bernardi and Alberto Lanconelli}, journal={arXiv: Probability}, year={2020} }

We propose a general method for studying existence and uniqueness of global strong solutions, as well as conditions for their extinction or persistence, for a large class of models, which includes the susceptible-infected-susceptible stochastic differential equation presented in \cite{Mao 2011}. Our method allows for a great flexibility in the choice of the coefficients of the equation, while preserving the essential features of several models from mathematical epidemiology. The approach…

## References

SHOWING 1-10 OF 14 REFERENCES

### A Stochastic Differential Equation SIS Epidemic Model

- MathematicsSIAM J. Appl. Math.
- 2011

It is proved that this classical susceptible-infected-susceptible epidemic model is formulated as a stochastic differential equation (SDE) for the number of infectious individuals and that this SDE has a unique global positive solution.

### A stochastic differential equation SIS epidemic model with two independent Brownian motions

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### On a Class of Stochastic Differential Equations with Random and Hölder Continuous Coefficients Arising in Biological Modeling

- MathematicsJ. Nonlinear Sci.
- 2019

It is proved the existence of a unique strong solution by means of a Cauchy–Euler–Peano approximation scheme which is shown to converge in the proper topologies to the unique solution.

### SDE SIS epidemic model with demographic stochasticity and varying population size

- MathematicsAppl. Math. Comput.
- 2016

### Stochastic Differential Equations And Applications

- Computer Science
- 2016

The stochastic differential equations and applications is universally compatible with any devices to read, and an online access to it is set as public so you can get it instantly.

### Brownian Motion and Stochastic Calculus

- Mathematics
- 2008

1 Preliminaries of Measure Theory De
nition 1 F P ( ) is said to be an algebra if (1) 2 F (2) A;B 2 F implies A S B 2 F (3) A 2 F implies AC 2 F . F is said to be a semialgebra or semi-ring is (1) ;?…

### Modelling with Stochastic Differential Equations

- Mathematics
- 1992

Important issues which arise when stochastic differential equations are used in applications are discussed in this chapter, in particular the appropriateness of the Ito or Stratonovich version of an…

### Exit boundaries of multidimensional SDEs

- MathematicsElectronic Communications in Probability
- 2019

We show that solutions to multidimensional SDEs with Lipschitz coefficients and driven by Brownian motion never reach the set where all coefficients vanish unless the initial position belongs to that…