Virtual society:model

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Basic Virtual Society

We first define a basic virtual society (BVS) as a set of populated and geo-referenced (located) households. Populated means that the households comprise the whole population of the country with its age and gender distributions in each voivodeship (data obtained from NCB). In other words, every individual from a population, described by its age and gender, is assigned to a particular household. Also, each household in the BVS has a geographic location assigned to it, or in other words, it is located. A schematic workflow for the generation of a basic virtual society is presented in Figure 1.

Fig.1: The workflow used to generate a basic virtual society. Data fr om NCB, i.e. number of households, age distribution of women and men, has a voivodeship resolution.

Once a basic virtual society is created, any additional infrastructural network can be developed using the same general workflow. First, specific outposts have to be located (in the lack of the geo-location data as in e.g. USA virtual society models of Ferguson et al[1] or Stroud et al[2] ). Then, agents have to be assigned to a particular outpost. Figure 2 presents a schematic workflow for the addition of schools and workplaces to the BVS.

Fig.2:The workflow used for the generation of the educational (schools) and employment (workplaces) infrastructure, and a subsequent assignment of agents to an appropriate institution. The numbers of different level schools, and the number of workplaces taken from NCB have a commune resolution. Primary and secondary schools, colleges, and workplaces are separated in the scheme because different methods were used for the populating of these institutions (see text).

A particular implementation of the general workflow from Figure 2 may differ in a way an agent assignment to particular outposts is done. Indeed, in these studies, this was done separately for primary and secondary schools, colleges, and workplaces. Typically, if the statistical data on geo-location and size of schools or workplaces are available, gravity models are used[1][2] for the agent assignment to the appropriate outposts. Otherwise, if the available or used data constrains only the total number of schools, workplaces (which is the case in this work) or the average school size, heuristic free-selection algorithms are implemented, e.g. allowing for the random selection of the school for each child under certain constraints [3][1][4].


Allocation of agents to the households

The age and gender distribution in every household is obviously not random, but rather it should reflect some possible relationships, the "generation gap". In order to reproduce realistic households populations, we propose a stochastic algorithm supporting a decision-making, necessary to place an agent in a household. We call this step a game, due to the conceptual proximity of this method to the methods commonly used within a framework of the game theory.


First, agents were divided into men and women and subdivided into 16 smaller populations appropriate for polish voivodeships. Then, for each gender and each voivodeship, agents were simply divided into age groups according to age distribution of the given gender in the given voivodeship (these data were acquired from Polish NCB). Subsequently, agents were distributed among households separately in each voivodeship.TO BE CHECKED!!!. Second, the size of household was chosen randomly from the distribution of household sizes in Poland (data taken from NCB).TO BE CHECKED!!!


To assign a software agent (of a given age and gender) to a household, the following rules were devised:

Fig.3: Probabilities used during the households populating.
  • Children (age 0-24) and parents were treated separately.
  • Children were not placed in empty households.
  • For each member in the household (if existing), the probability of attraction (denoted as p_a) or competition (p_c) between given member and the agent to be placed were calculated. The probabilities, shown in Figure 3, were chosen arbitrarily, and were dependent only on the age difference, τ, between a given household-member and the agent to be placed. To give an example, a child-aged agent was placed in a household only if there was already a parent-agent in this household, and only if this agent was old enough to be a parent of this particular child to be placed. There were 3 kinds of attraction probabilities, and one competition probability:
    • the probability of an attraction between child and adult female, p_{a}(\tau_{child-female}), where \tau_{child-female} = age_{female} - age_{child}; It was set to zero for the age difference less than 15 (to allow for "generation gap", that is, to ensure that mother is at least 15 years old). The highest pawas for age child-female age difference equal 26 - the number reported as the average age of a woman giving birth to her first child.
    • the probability of an attraction between child and adult male, p_{a}(\tau_{child-male}), where \tau_{child-male} = age_{male} - age_{child}; It was set to zero for the age difference less than 18.
    • the probability of an attraction between adult female and adult male, p_{a}(\tau_{female-male}), where \tau_{female-male} = age_{male} - age_{female};
    • the probability of a competition between adults of the same gender, p_{c}(|\tau_{ss}|), where |\tau_{ss}| is the absolute age difference between the agent to be placed and a given household member of the same gender; Only the maximum p_a and p_c from all obtained within a given household were used in further calculations.
  • The overall probability for acceptance of the agent in the given household was calculated using the following formula, p = max\{0; min\{1; \alpha + \beta p_a - \gamma p_c\}\}, where optimal values for \alpha, \beta, \gamma parameters were found to be 0.125, 0.9, and 0.7, respectively. The probability of placing an adult agent in an empty household equals 1.

Geo-location of the households

In order to locate a household taken from the set of households generated in the procedure described above, the following algorithm, based on the LandScan population density map, was applied: The number of inhabitants in each node of the LandScan map becomes this node's threshold value for the generated virtual population. Each node is filled with households' members by taking randomly a household from the subset of households corresponding to a given administrative unit (voivodeship in this case). Every time all household members are added to a given node. This continues while the total population in the node is below the threshold value from the LandScan map.

Allocation of agents to schools and workplaces

References

  1. 1.0 1.1 1.2 FERGUSON N M, D. A. T. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley, and D. S. Burke, Strategies for mitigating an influenza pandemic, Nature, 442 (2006), pp. 448-452
  2. 2.0 2.1 STROUD P, Del Valle S, Sydoriak S, Riese J and Mniszewski S (2007). Spatial Dynamics of Pandemic Influenza in a Massive Artificial Society,Journal of Artificial Societies and Social Simulation 10(4)9
  3. FERGUSON N M, D. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn, and D. Burke, Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature, 437 (2005), pp. 209-214
  4. GERMANN T C, K. Kadau, I. Longini, and C. Macken, Mitigation strategies for pandemic influenza in the United States, Proc. Nat. Acad. Sci., 103 (2006), pp.5935-5940