# Unifying incidence and prevalence under a time-varying general branching process

@inproceedings{Pakkanen2021UnifyingIA, title={Unifying incidence and prevalence under a time-varying general branching process}, author={Mikko S. Pakkanen and Xenia Miscouridou and Charles Whittaker and Tresnia Berah and Swapnil Mishra and Thomas A. Mellan and Samir Bhatt}, year={2021} }

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump–Mode–Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the…

## 3 Citations

### The uncertainty of infectious disease outbreaks is underestimated (preprint)

- Mathematics
- 2022

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). Majority of frameworks assessing infectious disease risk consider only…

### Incorporating testing volume into estimation of effective reproduction number dynamics.

- BiologyArXiv
- 2022

This work develops a new model that incorporates the number of diagnostic tests as a surveillance model covariate and demonstrates that incorporating tests leads to improved performance over the state-of-the-art.

### Estimating epidemiological quantities from repeated cross-sectional prevalence measurements

- MedicinemedRxiv
- 2022

Estimates of time-varying and static epidemiological quantities that were derived from the estimates published by ONS are presented, indicating that repeated cross-sectional studies make it possible to estimate epidemiological parameters from population-level models.

## References

SHOWING 1-10 OF 62 REFERENCES

### The point-process approach to age- and time-dependent branching processes

- MathematicsAdvances in Applied Probability
- 1983

The multitype age-dependent branching process in varying environment is treated as a random stream (point process) of the birth and death events. We derive the point-process version of the…

### On the Theory of Age-Dependent Stochastic Branching Processes.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1948

The problem is restricted to the special case where only binary transformations occur; that is, one particle can be transformed only into two others, and the methods employed are easily extended to deal with the general case with n-ary transformations.

### A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics

- Environmental ScienceAmerican journal of epidemiology
- 2013

This tool produces novel, statistically robust analytical estimates of R that incorporates uncertainty in the distribution of the serial interval and should help epidemiologists quantify temporal changes in the transmission intensity of future epidemics by using surveillance data.

### A Method for Obtaining Short-Term Projections and Lower Bounds on the Size of the AIDS Epidemic

- Medicine
- 1988

Abstract A methodology is proposed for obtaining short-term projections of the acquired immunodeficiency syndrome (AIDS) epidemic by projecting the number of cases from those already infected with…

### Estimating Individual and Household Reproduction Numbers in an Emerging Epidemic

- EconomicsPloS one
- 2007

It is argued that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation.

### Transmission potential of smallpox in contemporary populations

- MedicineNature
- 2001

Despite eradication, smallpox still presents a risk to public health whilst laboratory stocks of virus remain. One factor crucial to any assessment of this risk is R0, the average number of secondary…

### A note on generation times in epidemic models.

- MathematicsMathematical biosciences
- 2007

### Bayesian Inference for Contact Networks Given Epidemic Data

- Mathematics, Computer Science
- 2010

This article estimates the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts using a Bayesian framework and Markov chain Monte Carlo integration.