Abstract
A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.
Highlights
The mathematical modeling of different diseases continues to be an area of active research
The numerical simulation of the resulting stochastic differential equations (SDEs) is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods
The parameters are identifiable we study the correlation of parameters using Markov chain Monte Carlo sampler
Summary
The mathematical modeling of different diseases continues to be an area of active research. Epidemic modeling tries to relate disease dynamics at the population level to basic properties of the host and pathogen populations and of the infection process. These subdivisions of the population are called compartments This idea has been extended to SEIR epidemic model where the population can be partitioned into four compartments: susceptible (S), latent or exposed (E), infectious (I), and recovered (R). The mathematical modeling of SEIR diseases is largely done deterministically [1] [2] [3] [4]. The ODEs explain how a system changes or evolves, when the change occurs and the effect of the starting point to the initial solution and so forth Such modeling does not take into consideration some of uncertainties.
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