To explore whether existence of long-lasting partial immunity against reinfection with

A population-based mathematical model was constructed to describe

Partial immunity against reinfection was found necessary to explain observed

A strong long-lasting partial immunity against

An understanding of

Since

Against this background, we present a novel hypothesis-generation approach to assess the existence, and to provide a plausible effect-size estimate, of the partial immunity against reinfection. The approach rests on the concept that natural history effects at the individual level have manifestations at the population level. Starting from population-level measures, we used mathematical modelling to provide the link between these measures and natural history effects.

Although our approach uses an indirect method, mathematical modelling, its strength lies in that it provides an independent assessment of this effect that capitalises on existing quality population-based data. Specifically, we used two population-level distributions, prevalence by age and by sexual risk, to explore a population-level ‘signature’ of partial immunity. We also factored in the model different biological (eg, various forms of immunity and impact of treatment on immunity development) and behavioural (eg, impact of age on sexual behaviour and various forms of sexual mixing by age and risk behaviour) mechanisms that potentially may explain the observed patterns, irrespective of inclusion of an immunity effect. Accordingly, we aimed to answer two questions: (1) Is the existence of partial immunity against reinfection necessary to explain prevalence patterns by age and sexual risk? (2) How strong is the effect of partial immunity likely to be?

We constructed a population-based deterministic compartmental model to assess the role of long-lasting partial immunity in

We assumed that, by the time of infection clearance, asymptomatic individuals acquire short-term temporary (90 days) but full immunity against reinfection, per the recent Althaus

Meanwhile, symptomatic individuals do not acquire immunity and revert back to the fully susceptible state after clearance by treatment—treatment shortens infection duration in symptomatic individuals, thus reducing their chance to develop an adequate immune response.

Details on model structure, equations and parameterisation are in the

The model assumes a stable population with a balance between births and deaths. It further incorporates 20 age groups, each of which describes a 5-year age band in the population. Demographics for the UK and the USA were drawn from the United Nations Population Division databases.

Sexual activity lifespan extends in the model from ages 15 to 74, with sexual activity declining with older age. For each 5-year age category, the model incorporates six sexual risk groups describing a hierarchy of sexual risk behaviour varying from low to high levels. Accordingly, the model accommodates for the broad behavioural heterogeneity that typically exists in a given population.

Distribution of the population across risk groups is informed by data for the number of heterosexual partners during the last 12 months, as reported in the second UK National Survey of Sexual Attitudes and Lifestyles (Natsal-2).

The pattern of sexual mixing between sexually active individuals is determined by two mixing matrices describing the likelihood of a partnership to be formed based on age group or risk group.

Details on the inclusion of demography and sexual behaviour in the model are in the online supplementary materials.

The model was parameterised using available data for

Summary of description and results of the sensitivity analyses with respect to variations in model structure

Sensitivity analysis | Description | Result |

1. Variation in the distribution of risk behaviour across risk groups.* | Explored the impact of variation in the distribution of risk behaviour across risk groups by varying (in univariate analysis) the parameter
σ
of the distribution of risk behaviour ( | The predicted age-specific |

2. Variation in the sexual mixing by age.* | Explored the impact of variation in sexual mixing by age (in univariate analysis) across the full spectrum starting from proportionate mixing-up to fully assortative mixing. This was done by varying | The predicted age-specific |

3. Variation in the sexual mixing by risk.* | Explored the impact of variation in sexual mixing by risk (in univariate analysis) across the full spectrum starting from proportionate mixing-up to fully assortative mixing. This was done by varying | The predicted age-specific |

4. Temporal variation in risk behaviour. | Explored the impact of temporal variation in risk behaviour on our estimated partial immunity strength by assuming that 10% of individuals change their risk group every year. | α for the UK data was estimated at 93% (95% UI: 89%–95%) with an uncertainty analysis median of 93%—similar to the original estimate. |

5. Removal of latent period in | Explored the impact of removing the latent period in | α for the UK data was estimated at 93% (95% UI: 88%–97%) with an uncertainty analysis median of 93%— similar to the original estimate. |

6. Inclusion of partial immunity for the symptomatically infected individuals. | Explored the impact of inclusion of partial immunity for the symptomatically infected individuals. | α for the UK data was estimated at 93% (95% UI: 89%–96%) with an uncertainty analysis median of 93%— similar to the original estimate. |

7. Variation in the duration of the short-term temporary but full immunity. | Explored the impact of varying the duration of the short-term temporary but full immunity over a range of 0–100 days. | Variation in the short-term temporary immunity had limited impact on the estimated effect size of partial immunity ( |

All sensitivity analyses were applied to the model fit of the UK data.

*Conducted in view of the fundamental ambiguity in defining ’sexual risk’,

UI, uncertainty interval.

We conducted analyses to explore the role of partial immunity in explaining observed

We generated model predictions for the age-specific and sexual risk-specific distributions of

The strength of the long-lasting partial immunity against reinfection (
α
) was estimated by fitting model predictions to data from the following surveys: (1) UK age-specific

The uncertainty intervals (UIs) for
α
estimates were calculated through multivariate uncertainty analyses with respect to variations in the model’s sexual behaviour structure. This was done using Monte Carlo sampling from (conservatively) uniform probability distributions, assuming 20% uncertainty around the parameters’ point estimates, as informed by the range of available data and previous modelling studies.

Several sensitivity analyses were conducted with respect to variations in model structure. These are summarised in

We assumed, for theoretical simplicity, that the partial immunity mechanism is a reduction in the susceptibility to reinfection. However, there is ambiguity about the exact mechanism(s).

Methodological details of these analyses are in the online supplementary materials.

To derive a plausible estimate for the effect size of
α
, we fitted

Model fits for

Sensitivity analyses of the impact of alternative biological mechanisms, for the effect of partial immunity, on the model-predicted age-specific

We explored the role of immunity in

The presented analyses highlighted how a natural history effect that occurs at the individual level (ie, development of partial immunity) expresses itself indirectly as an observed effect on prevalence patterns at the population level—thereby facilitating a derivation of a plausible estimate for the effect size using a population-level mathematical model. The immunity effect led to high prevalence in youths, with rapid decline in prevalence with age, testifying to age being a strongly predictive risk factor for

The observed strong immunity effect is consistent with existing direct evidence from animal studies

The sensitivity analyses of alternative mechanisms for the immunity effect indicated that infectiousness reduction cannot explain observed patterns (

Limitations may have affected this study. Although an elaborate model was used to capture the complexity of

Despite these limitations, the model was sufficiently complex to incorporate the main factors that can affect our research questions, and produced robust fits for

In conclusion, we explored the existence of partial immunity against

Partial immunity against C

Immunity mechanism can be either a reduction in susceptibility to reinfection or a reduction in infectious-period duration upon reinfection, or a combination of both.

The authors gratefully acknowledge Professor Nicola Low from the University of Bern for valuable insights and rich discussions and critically reviewing this study. The authors also gratefully acknowledge the fine support of Ms Adona Canlas in the conduct of this study. The authors are further grateful for infrastructure support provided by the Biostatistics, Epidemiology, and Biomathematics Research Core at Weill Cornell Medicine-Qatar.

Katy M E Turner

RO conceived the study, developed the mathematical models and conducted the analyses. HC contributed to data analysis and wrote the first draft of the article. CLA provided technical input. LJA-R led the study design and analyses. All authors contributed to results generation and interpretation and to writing of the article.

RO acknowledges the support of Precursory Research for Embryonic Science and Technology (PRESTO) grant number JPMJPR15E1 from Japan Science and Technology Agency (JST), and Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Young Scientists (B) 15K19217. This publication was made possible by NPRP grant number 5-752-3-177 from the Qatar National Research Fund (a member of Qatar Foundation). The findings achieved herein are solely the responsibility of the authors.

None declared.

Not required.

Not commissioned; externally peer reviewed.

Model equations and parameters are provided in the online supplementary materials.