Table 2 Description of the symbols used in the mathematical formulation of the transition probabilities for describing the agent based model

N

Total number of individuals in the cohort (10,000 individuals considered as a population cohort)

S(t); E(t); I(t); R(t)

Number of individuals in the Susceptible, Exposed, Infectious, and Recovered states at time point t

P _external (t)

Probability of a susceptible individual acquiring infections from contacts in society

 P _family (t)

Probability of a susceptible individual acquiring infections from contacts within household

v

Baseline infectivity of a given pathogen. Always present in determining the probability of acquiring an infection by a susceptible individual (Fixed at 0.025 for each day)

(I(t))/N

Proportion of infectious individuals in society at time t. Impacts the probability of susceptible individuals acquiring infections from society at time t + 1

P ₀

Influx of infection from outside of the studied population to avoid permanent extinction of the epidemics (fixed at 0.0001 for a single day)

z

Pathogen specific reduction factor; Expression of severity of symptoms thus extent of isolation from the society; Multiplicative factor on the sum of the proportion of infectious individuals and the influx of infections from outside the population (Range: 0.3–0.9)

s(t)

Seasonality parameter at time point t; expression for the seasonal variability in the transmission probability of the infection from contacts at the society level for a specific pathogen

A

Amplitude for the seasonality characteristics of the pathogen; indicates the extent of seasonal variation of transmissibility of a given pathogen (Range: 0.5–5, lower values indicate lack of seasonality whereas higher values are indicative of seasonality)

c

Factor for increased closeness of contacts within household as differentiated from the society contacts; Multiplicative factor on the baseline infectivity for determining the within household transmission probability for a specific pathogen (Fixed at 9 for all pathogens)

Λ

Coefficient for the degree of household isolation. In case of complete pathogen dependency with full household isolation of 100%, risk of acquiring infections from outside household when already infectious is zero. For the independent pathogens scenario, the household isolation is 0% which means that there is a complete risk of acquiring a co-infection from outside household.

t ₀

Coefficient for the phase shift. It helps in varying the temporal trend of the pathogen. It is set to zero for most cases. Except for pathogen 10, we examine the case when the value is +/− 45 days and remains zero for the other pathogens

I _h (t)

Number of infectious persons in the same household at time t; impacts the probability of acquiring an infection from household contacts at time t + 1; exponential factor on the product of baseline infectivity and closeness of contacts

LP

Length of asymptomatic infection(latency period);Average time spent from being exposed to becoming infectious for a specific pathogen (Range: 1–6)

IP

Length of symptomatic infections(infectious period); Average time spent in-between becoming infectious and acquiring immunity (Range: 2–9)