Application of a Second-order Stochastic Optimization Algorithm for Fitting Stochastic Epidemiological Models
In public health, it is critical to have a reasonable understanding of an epidemic disease in order to set pragmatic goals and design highly-impactful and cost-effective interventions. Mathematical models of these epidemiological processes can support decision making by forecasting disease spread in space and time, and by evaluating intervention outcomes many times in-silico before spending valuable resources implementing real-world programs. Recent efforts in computational epidemiology have focused on the design and application of detailed stochastic models that capture physical mechanisms through which disease propagates, along with the statistical fluctuations inherent in complex systems. These stochastic models are readily available, and recent work has focused on applying these models to malaria (Eckhoff et al. 2016, Eckhoff 2013, Marshall et al. 2016, Gerardin et al. 2016), HIV (Bershteyn et al. 2016, Eaton et al. 2015), polio (McCarthy et al. 2016, Grassly et al. 2006), and more.
Some types of diseases with permanent immunity, such as measles, mumps and rubella, can be described as Susceptible-Infected-Recovered (SIR) model. In this model each individual can only exist in one of the discrete states such as susceptible (S), infected (I) or permanently recovered (R). We have two transitions in this case. An infected person can infect others with an infection rate, β, and is cured with curing rate, δ. Therefore, the parameters of our model are θ = (β,δ). Our objective, here, is finding a good model for the given epidemic data, i.e. infection rate and curing rate, to investigate the properties of the disease spread. These properties will allow the researchers to learn about the diseases, and thereby enabling them to test competing theories about transmission of disease and to devise better containment strategies.
Figure 2: (a) Comparison of the number of iterations for convergence for conventional SPSA and PSPO.(b) Number of iterations vs. number of parallel computing rounds, M, in PSPO.