Table 2a.

components and main findings of typhoid transmission models.

	First author and year		Model type	Disease states	Data source(s)	Fitting process	Interventions modelled	Time horizon	Sensitivity analysis	Findings	Comments
1	Cvjetanović 1971, 1978	[18],[19]	Compartmental deterministic with births = deaths, without age-structure	N S Es Ea Is Ia Ct Cl Rt Rl	Parameters estimated using literature and expert opinion. Considers an eidemiological scenario approximating Western Samoa.	None	Vaccination with whole-cell inactivated vaccines, VE 60%, 75% or 90%, coverage 60, 80 or 100%. As one-off or 5 yearly campaigns. Sanitation	60 years	Epidemiological/clinical parameters fixed. Effective contact rate (per capita per day) varied.	For both low and high VE, single vaccination campaigns achieve temporary reduction in incidence rates before return to a rate determined by the force of infection, where force of infection is above an elimination threshold. Sustained reduction in force of infection reduces incidence. Multiple vaccination campaigns reduce incidence will campaigns are sustained.	Multiple parameters are included without fitting. Outputs should be considered illustrative.
2	Briscoe 1980	[22]	Deterministic analytical SIS	S I	N/A	N/A. Reviews Cvjetanović models. Analysis of role of force of infection and recovery on equilibrium prevalence.	N/A	N/A	N/A	Force of infection determines prevalence, and vice versa. Stochasticity may prevent disease eradication.	Intended as an analytical model rather than epidemiological simulation.
3	Bailey 1982	[23]	Compartmental deterministic with births = deaths, without age-structure	S E I C R	[18]	Rule-based simplification of Cvjetanović 1971 model [18] with direct mathematical solution of steady-state equations.	N/A	N/A	N/A, suggests an approach to sensitivity analysis [26]	For a steady-state model, structural simplification results in compartment population estimates consistent with the unsimplified model for a given effective contact rate.	Reducing the number of compartments makes a model more suitable for validation with data.
4	Cvjetanović 1986	[20]	Age-structured compartmental deterministic SIRS. Birth and death rates from Chile	N S I Ct Cl Rt Rl	Demographic and typhoid surveillance data for Santiago and rest of Chile	Effective contact rate per capita per unit day (age-specific for acquisition) from linear interpolation of age-specific incidence. Visual goodness-of-fit. Strong assumption that 20% of all cases are clinical.	Vaccination with Ty21a, 95% VE at 75% or 95% coverage of under 25s with 5 yrly revaccination. Food sanitation in schools reducing force of infection by 1/3 in ages 6 to 16 y. Sanitation with annual 2% or 5% improvement in force of infection over 10 years.	Interventions analysed over 25 y after run-in to equilibrium.	None	Vaccination campaigns would reduce age-specific incidence and increase the age of peak incidence Vaccination would not eliminate disease over 25 y but would result in year on year reduction in incidence if sustained. 10 y sanitation campaigns likely to reduce prevalence and continue to reduce prevalence after cessation.	Somewhat simplified model structure, though now age structured. The model is not validated sufficiently against data, nor are outputs sufficiently clear to make strong policy conclusions. Age-based changes in incidence with vaccination are consistent with epidemic theory.
5	González-Guzmán 1989	[21]	Compartmental deterministic SIS structure with births and deaths	S I V with environmental transmission	Parameter estimates for Chile	None, analytical model	Reductions in combinations of:  carrier prevalence  indirect contact rate  direct contact rate  environmental life of the bacterium  bacterial count in the environment. Vaccination with Ty21a, coverage scaled for equivalence to VE 74% or 95%.	10 y	N/A	Decline in incidence is not rapid, even with highly effective combined control measures. Reduction in chronic carriage most effective control procedure. Vaccination as a permanent programme would require a high proportion of the population to become immune to control typhoid within a meaningful timeframe.	Author cautions against using the model to estimate the effect of a vaccination programme but that it indicates areas for further epidemiological parameter determination.
6	Saul 2013	[25]	Individual-based stochastic, random-mixing.	S E Is Ia Ct Cl Rt Rl, Rc,;Rs; Vc Vs	Surveillance data from Dhaka, Bangladesh, and Kolkata India. Migration, birth and death rates from Matlab, Bangladesh. Other parameter from literature and expert opinion.	Maximum likelihood and visual inspection	None	40 y to equilibrium and 40 y follow-up. 20 y for effects of carriage.	Sensitivity analysis on refractory period from birth.	Distinguishes between sterile immunity and clinical Immunity (in which individuals can be infected but not develop disease). Multiple infections needed to develop sterile immunity. Natural immunity is likely to be long-lasting but needs further field investigation. Carriage stabilises dynamics, and is particularly important in lower incidence settings.	Complex agent based model, limited availability of epidemiological data results in issues of parameter identifiability. Plausible combinations of parameters identified.
7	Pitzer 2014	[24]	Compartmental, age-structured deterministic	S1 S2 I1 I2 R C W	Surveillance case series, Vellore, Tamil Nadu, India	Two-stage fitting with Latin hypercube sampling of starting parameters. Maximum likelihood estimation, simplex method.	Vaccination with: Ty21a, (VE 48%, duration = natural immunity), Vi polysaccharide (VE 80%, 3 y), Vi conjugate (VE 95.6%, 19.2 y). Vaccination of school age children as a campaign, routine vaccination of 6 year olds, or both together. Improvements in water and sanitation over 30 y	50 y to quasi-steady state and 25 y follow-up	Multi-parameter sensitivity analysis in model fitting.	Basic reproduction number is around 3 in Vellore and 7 in Dhaka. Natural immunity is likely to be long-lasting. Vaccination campaigns would not eliminate disease in Vellore but instead see disease rebound in 5 to 10 y. A campaign plus routine immunisation could result in a new lower incidence disease state. High baseline carriage rates reduce the indirect protection of vaccines–understanding carriage prevalence should be a disease control priority. In most circumstances modelled, improvements in hygiene and sanitation have more impact than vaccination.	Best fitting parameter sets were highly sensitive to initial parameter selection. Identifies carrier transmissibility and relative contributions of short- and long- cycle as import epidemiological sources of uncertainty.

VE = vaccine efficacy. Effective contact rate is the rate at which two individuals come into contact per unit time, with the nature of the contact being such that if one was infectious and the other susceptible, infection would be transmitted.