Stochastic SIR Household Epidemic Model with Misspecification

The stochastic SIR household epidemic model is well discussed in [3], [4], [5] and also in [1]by assuming that the infection period distribution is known. Sometimes this may wronglybe assumed in the model estimation and hence the adequacy of the model fittness to thefinal size data is affected. we examined this problem using simulations with large population size and theoretical parameters in which the final size data is first simulated with exp(4.1) infectious period distribution and estimated with Gamma(2,4.1/2) infectious period distribution and vice versa. The estimates of the two dimensional models are further explored for a range of local and global infection rates with corresponding proportion infected and found to be biased and imprecise

Inference of the Stochastic SIR Household Epidemic Model with Misspecification and Misclassification.

Sometimes the final size epidemic data may be misclassified and the infectious perioddistribution also misspecified. How are the estimates affected when these two scenarios occur and hence the adequacy of the model fittness to the final size data, is the focus of this study. This is investigated using simulations in the face of global infection, by first simulating the final size epidemic data with exp(4.1) infectious period distribution and estimated with Γ(2,4.1/2) infectious period distribution, vice versa.The estimates are further explored for a range of local and global infection rates andcorresponding proportion infected, misclassification probabilities in the permissible region.The three and four dimensional models are found to be significantly better than the twodimensional model given these scenarios

Effects of minimum epidemic and population sizes on a global epidemic in simulations of final size data

The stochastic SIR household epidemic model is well discussed in [2], [3] and [4]. The work of [1] also proposed maximum likelihood based algorithm for its inference by assuming independence of epidemic in each household, contrary to the dependency assumption in [4].Using simulations, we examined the need for an appropriate choice of cut-o between small and large epidemics often referred to as minimum epidemic size, using rejection sampling, for a global infection to occur and then compared the estimates of the model parameters over a range of theoretical parameters, LambdaL and lambdaG with corresponding z in [0; 1]:We found that with large population size, appropriate choice of the minimum epidemic size and lambdG not 0, facilitate the occurrence of a global epidemic.Thus, given these scenarios, the adequacy of the model fitness to the final size epidemic data is then realised

The Stochastic SIR Household Epidemics With TI ≡ 4:1 and TI Having GAMMA(a, b) Infectious Period Distribution

Model estimates, their functions are in no doubt affected by wrong choice of the infectious period distribution, TI when the actual one is unknown. This is a misspecification problem which is often accompanied with biased and imprecise estimates. This work does not com- pletely examined this problem but explored the choice of constant infectious period, TI ≡ 4.1 and TI distributed as Γ(2, 2.05) for the household epidemic and then examined their effects on the behaviours of the model functions and quality of its maximum likelihood estimates in order to see if there are considerable disparities in the maximum likelihood estimates and behaviours of the functions giving these scenarios and whether constant infectious period is a reasonable assumption for the stochastic SIR household epidemic. &nbsp

Validating Numerical to Theoretical Solutions in a Reaction-Diffusion with Linear Cross-Diffusion Systems.

In this paper, we consider a reaction diffusion system with linear cross-diffusion. We carry out the analytical study in detail and find out that, when the diffusion coefficient is unity, Turing instability does not occur, but with the introduction of cross-diffusion, the system exhibit Turing instability. The numerical results reveal that, on increasing the value of gamma, there is an occurrence of spatial patterns which conforms with the theoretical results. The cross-diffusion coefficients really plays a vital role on the parameter spaces and spatial patterns of our system