(A) Flowchart of a compartmental model illustrating the main stages of infection for an S-E-I-R-S system, following pathogen abundance over time. The transmission process begins when the susceptible host (S) is exposed to the pathogen. Following inoculation, the host is considered infected but does not transmit the pathogen (exposed/latent phase (E)). Exposed individuals become infectious to others if they shed a sufficient quantity of pathogen (I). Over time the pathogen number declines if adequately controlled by the host immune system, successful treatment or natural death. Depending on the agent, the host can therefore recover and become immune (R) for life, or develop immunity for a limited time and become susceptible again (S), or eventually leave the population (death). The host develops symptomatic disease some time after infection depending on the duration of the incubation period (time period between infection and disease). In the flow chart, each compartment represents the number of individuals in the given infection state at time t (state variable). The arrows, quantified by state-specific parameter in Eqn 1 (B), represent the flow of individuals from one state to another. A higher degree of complexity can be included by adding additional compartments (eg, typically three compartments are used to reflect the three main infectivity stages of HIV infectivity/infection: acute/primary, low/asymptomatic, medium/symptomatic). Figure adapted from Aron.63 (B) Differential equations translating a S-E-I-R-S deterministic model into mathematical terms. Each equation represents the change in the state variables at time t, which depends on the number of individuals in each compartment and the value of the parameters quantifying the flow between compartments. The flow of individuals between stages of infection occurs at an average state-specific per capita rate: rE=rate of becoming infectious, rI=rate of developing protective immunity, rL=rate of loss of immunity, rate of deaths=rR. The force of infection, λ(t), is intrinsically dependant on the number/prevalence of infectious individuals in the population, β (the per contact transmission probability) and c′ (contact rate). The parameter Λ represents the renewal of new susceptible hosts with Λ=0 for closed population and Λ>0 for open population. For a constant population, Λ=rRN(t) (that is, births equal deaths per unit time). Depending on the model complexity, the rate of flow between states (parameter) can be a fixed value, a function of other state variables, or change with time.