Abstract*Actuaries are often asked to provide a range or confidence level for the loss reserve along with a point estimate. Traditional methods of loss reserving do not provide an estimate of the variance of the estimated reserve, and actuaries use various ad hoc methods to derive a range for the indicated reserve. We use a Monte Carlo simulation method to compare various loss reserve estimation methods, including traditional methods and regression-based methods of loss reserving.
Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number R v , which is determined by the next-generation approach and obtained that if R v ≤ 1, the diseasefree equilibrium exists and it is locally as well as globally asymptotically stable. Further for R v > 1, a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
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