CTrace: Language for Definition of Epidemiological Models with Contact-Tracing Transmission

Abstract

In this work, we present our results in development of a domain-specific programming language for an agent-based infectious disease spread modeling with contact tracing transmission. We performed an analysis of methods and tools, accessible to a scientific community, which showed significant problems of currently developed approaches. Some methods provide significant performance, sacrificing ease-of-use, others offer simple programming interface but suffer with performance drawbacks. To address both of these issues, we designed a domain-specific programming language with simple and yet powerful syntax and minimal amount of boilerplate code. The chose of the underlying infectious disease spread model is based on a growing interest in agent-based models, which are becoming more popular due to higher simulation accuracy compared to classical compartmental models. At its core, each agent has its personal user-defined daily schedule, which dictates where the agent is situated at each simulation step based on numerous parameters, such as simulation “day”, agent’s inner state, inner states of linked to this agent compartments, which can be, for example, its house, place of work, school, etc. The underlying language’s engine uses this schedule to check, which agent pair were in contact with each other and where at each simulation step. The infectious disease, defined by a set of rules, which control how do these contacts affect inner states of both agents and how disease progresses in context of a single infected agent. We designed a compiler with Python as intermediate language for a simple programming interface and Numba support for machine language translation. Performed tests showed, that the language is capable of describing complex epidemiological models and the compiler is able to generate machine code efficiently enough to run simulations with medium number of entities. The main problem of a developed approach is the quadratic nature of algorithmic complexity of a contact tracing transmission process. We left optimization of it as a topic for a future research.

A Appendix

Here, we describe a formal grammar of a developed language.

The set of terminal symbols is defined as: $\varSigma =\{0..9,a..z,A..Z,+,-,*,/,^,==,!=,$ $<>$,<,>,$<=$,$>=$,$=,(,),\{,\},[,],.,~,\$$,$->$,$<-$,$|\}$.

The set of non-terminal symbols is defined as: $N=\{$“letter”, “digit”, “number”, “id”, “expression”, “program”, “distribution_declaration”, “distribution_disc_declaration”, “distribution_cont_declaration”, “function_ declaration”, “param_declaration”, “param_sampling”, “struct_declaration”, “transition”, “infection” $\}$.

The start symbol S is “program".

Production rules, presented using railroad diagrams, are defined in Figs. 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21.

Fig. 6.

Definition of letter non-terminal.

Fig. 7.

Definition of digit non-terminal.

Fig. 8.

Definition of number non-terminal.

Fig. 9.

Definition of id non-terminal.

Fig. 10.

Definition of program non-terminal.

Fig. 11.

Definition of $function\_declaration$ non-terminal.

Fig. 12.

Definition of $function\_declaration\_arguments$ non-terminal.

Fig. 13.

Definition of $param\_declaration$ non-terminal.

Fig. 14.

Definition of $distribution\_declaration$ non-terminal.

Fig. 15.

Definition of $distribution\_disc\_declaration$ non-terminal.

Fig. 16.

Definition of $distribution\_cont\_declaration$ non-terminal.

Fig. 17.

Definition of $param\_sampling$ non-terminal.

Fig. 18.

Definition of $struct\_declaration$ non-terminal.

Fig. 19.

Definition of infection non-terminal.

Fig. 20.

Definition of expression non-terminal.

Fig. 21.

Definition of transition non-terminal.