SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Cost-effectiveness of introducing the 10-valent pneumococcal conjugate vaccine into the universal immunisation of infants in Brazil

Background Cost-effectiveness studies have been increasingly part of decision processes for incorporating new vaccines into the Brazilian National Immunisation Program. This study aimed to evaluate the cost-effectiveness of 10-valent pneumococcal conjugate vaccine (PCV10) in the universal childhood immunisation programme in Brazil. Methods A decision-tree analytical model based on the ProVac Initiative pneumococcus model was used, following 25 successive cohorts from birth until 5 years of age. Two strategies were compared: (1) status quo and (2) universal childhood immunisation programme with PCV10. Epidemiological and cost estimates for pneumococcal disease were based on National Health Information Systems and literature. A 'top-down' costing approach was employed. Costs are reported in 2004 Brazilian reals. Costs and benefits were discounted at 3%. Results 25 years after implementing the PCV10 immunisation programme, 10 226 deaths, 360 657 disability-adjusted life years (DALYs), 433 808 hospitalisations and 5 117 109 outpatient visits would be avoided. The cost of the immunisation programme would be R$10 674 478 765, and the expected savings on direct medical costs and family costs would be R$1 036 958 639 and R$209 919 404, respectively. This resulted in an incremental cost-effectiveness ratio of R$778 145/death avoided and R$22 066/DALY avoided from the society perspective. Conclusion The PCV10 universal infant immunisation programme is a cost-effective intervention (1-3 GDP per capita/DALY avoided). Owing to the uncertain burden of disease data, as well as unclear long-term vaccine effects, surveillance systems to monitor the long-term effects of this programme will be essential.