My name is Nazila Akhavan and I work as a Mathematical and Statistical application developer at Kings Distributed Systems. I port and implement Mathematical programs over the Distributed Compute Protocol in Distributed Compute Labs.
Basically, I work on the R package pomp (King et al. 2016) which provides us with a wide range of functions to represent models that help to have a better realization of nonlinear partially-observed Markov processes. The package is used to simulate, analyze, and fit the model to data. The motivation, structure, and contents of the package are described, with examples, in Journal of Statistical Software paper. The aim is to make the package adaptable with DCP protocole and implementable in DCP workers.
When dealing with large populations deterministic models are often used. In deterministic compartmental models, the transition rates from one compartment to another are mathematically expressed as derivatives. Hence the model is formulated using ordinary differential equations (ODE), Kermack WO . Trajectory matching attempts to match trajectories of a deterministic model to data. In fact, the function estimates the parameter of the model by fitting the trajectory to data. It maximize the likelihood of the data assuming there is no process noise and all stochasticity is measurement error. The R package pomp provides useful tools for trajectory matching.
We provide the grafical interface of trajectory matching which is available at https://trajmatch.apps.distributed.computer.
This method is a very popular class of algorithms to solve estimation problems numerically when recursively as observations become available, and is routinely used in fields as diverse as biology, computer vision, econometrics, robotics and navigation.
The function is implementing the "maximum likelihood by iterated, perturbed Bayes maps" which is an improved iterated filtering algorithm for estimating the parameters of a partially-observed Markov process.
Mathematical modeling in epidemiology
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. Models use some basic assumptions and mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programes. The modelling can help in deciding which intervention(s) to avoid and which to trial.
Infectious diseases of humans have been well-documented in literature and historical records due to their sometimes calamitous effects on civilizations. The effect of a disease on a population varies, depending on the structure of the population (rural or urban, aging or young, easy or difficult access to health care), and the history that the community has had with the specific disease. Mathematical and statistical tools have been used to describe the dynamics of infectious diseases.The modeling of infectious diseases is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic.
N. Akhavan Kharazian, F. M. G. Magpantay. The honeymoon period after mass vaccination[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 354-372. doi: 10.3934/mbe.2021019