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by Hélène Arduin (Submitted: 03/08/2018)

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We aim to simulate the co-circulation of influenza and another pathogen, interacting with each other at the host level in a virtual human population. Interactions with influenza and their consequences can vary according to several characteristics of the other pathogen at stake. Here we identified two groups of pathogens: some causing annual regular outbreaks but absent most of the year, and some that are endemically present in the population throughout the year. We implemented a simulator with two models based on the same core structure: one to represent the co-circulation of an influenza virus and an endemic pathogen, the other representing the co-circulation of an influenza virus and an epidemic pathogen.

This model is the one with the endemic pathogen.


Each individual is characterized by several state variables: age, a series of variables regarding their infectious status for influenza, and a series of variables regarding their infectious status for the second pathogen.


The simulator time step unit is a day. The mean duration of all the possible states regarding the two pathogens have to be set by the user through several buttons. During the simulation, the true duration of a state for each individual getting infected is drawn from a gamma distribution of mean the value set by the user.

For the first pathogen we provide parameters’ values corresponding to influenza natural history: the incubation period has a mean duration of two days and is followed by a symptomatic phase with a mean duration of four days. During these two states, an individual is contagious starting the second day of influenza presence and ending two days after the beginning of symptoms. After the symptomatic period, we chose in our simulator to immunize the individual to this year’s influenza virus.

The same scheme applies to the second pathogen. The user has to define the mean durations of the asymptomatic and symptomatic phases, the duration of the contagious period, and the possible immunity after infection.


The model is spatially explicit. The individuals can move in what is referred to as a “world” in the NetLogo software. Here it is a torus, which is divided in patches. Two persons are considered in contact if they coincide on the same patch during a given time step. The dimension of the patches – and thus of the world – is set in order to have, on average, 13 contacts per person and per day.


During each time step, six procedures are executed in a given order:

1. reset of the daily new cases counters for each pathogen
2. set of the characteristics (on the first day of the year) and launch of the current year’s epidemics of influenza and of the other pathogen if it is an epidemic one (on the chosen first days of the outbreaks)
3. transmission of influenza
4. transmission of the second pathogen
5. global processes:
a. reproduction of humans
b. aging
c. status update regarding influenza
d. status update regarding the second pathogen
e. counters update for the different pathogens states’ durations
f. move of individuals in the world
6. update of the daily new cases counters


Different interaction mechanisms are embedded in our model. They are based on the several biological mechanisms which were found in literature, and summed up into different macroscopic mechanisms in order to be implemented in the model.

Two mechanisms are common to both SimFI models: “acquisition” and “transmission”, and each model also have another interaction mechanism specific to the second pathogen’s nature: “cross-immunity” has only been observed in the case of two viruses co-circulating (SimFI-Epi), and “pathogenicity” has only been encountered when an epidemic and an endemic pathogens co-circulate (SimFI-End).

### Direction
Each mechanism can represent either an interaction from influenza on the second pathogen or the other way around, except for the “pathogenicity” interaction which is only an action of influenza on the endemic pathogen.

### Acquisition interaction
When already infected with one pathogen, one has a modified probability to be infected with the other pathogen during a certain period of time.
### Transmission interaction
When infected by the two pathogens, one has a modified probability to transmit the pathogens to susceptible others.

### Cross-immunity interaction
When immune to one pathogen, one has a modified probability to be infected with the other pathogen.

### Pathogenicity interaction
When infected by influenza and in the asymptomatic period of the endemic pathogen, one has a modified probability to develop an infection with the second pathogen.


All random numbers and probabilities of transmission, acquisition and infection for both pathogens are randomly chosen (see below).


NetLogo uses a random number generator to provide pseudo-random numbers which are determined by the choice of a seed at the beginning of each new simulation.


NetLogo offers different visualization solutions like plots and variable monitors while the simulation is running, or recording of chosen variables values at each time step at the end of a simulation. By default, our simulator records the daily number of new symptomatic cases for influenza and the other pathogen.


Upon initialization the individuals are uniformly distributed at random around the world, with uniformly distributed ages. All individuals are healthy. In the SimFI-End model, a number of randomly chosen individuals get infected with the endemic pathogen, according to the value set by the user.


At the beginning of each simulated year, the immunity from the past year is reset for all individuals and the characteristics for the epidemics pathogens are drawn from probability distributions: importation date, number of imported cases, infectiousness, and proportion of immune individuals at the beginning of the new season.


All default values are meant to reproduce the natural history of influenza virus and Streptococcus pneumoniae as second pathogen. The years are defined as starting on September 1st (ticks = 1 [364]) and ending on August 31st (ticks = 0 [364]).


This model was originally based on the Virus model from the NetLogo library.

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