Inference on a stochastic SIR model including growth curves
提出一个包含布朗运动随机性和种群增长函数的SIR模型，用准极大似然估计法进行参数推断，并通过模拟评估三种增长曲线下的估计效果。
A Susceptible-Infected-Removed stochastic model is presented, in which the stochasticity is introduced through two independent Brownian motions in the dynamics of the Susceptible and Infected populations. To account for the natural evolution of the Susceptible population, a growth function is considered in which size is influenced by the birth and death of individuals. Inference for such a model is addressed by means of a Quasi Maximum Likelihood Estimation (QMLE) method. The resulting nonlinear system can be numerically solved by iterative procedures. A technique to obtain the initial solutions usually required by such methods is also provided. Finally, simulation studies are performed for three well-known growth functions, namely Gompertz, Logistic and Bertalanffy curves. The performance of the initial estimates of the involved parameters is assessed, and the goodness of the proposed methodology is evaluated.