skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity
This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection.  more » « less
Award ID(s):
1928930
PAR ID:
10432427
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Symmetry
Volume:
14
Issue:
11
ISSN:
2073-8994
Page Range / eLocation ID:
2288
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; ; ; (, Vaccines)
    COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the Canadian population. This is the first mathematical model to do so. We estimate that 60–80% of the Canadian population has some immunity to COVID-19 by late Summer 2021, depending on specific characteristics of the vaccine and the waning rate of immunity. Models results indicate that increased vaccination uptake in age groups 12–29, and booster doses in age group 50+ are needed to reduce the severity COVID-19 Fall 2021 resurgence. 
    more » « less
  2. ; ; (, Journal of medical virology)
    One of the most consequential unknowns of the COVID-19 pandemic is the frequency at which vaccine boosting provides sufficient protection from infection. We quantified the statistical likelihood of breakthrough infections over time following different boosting schedules with messenger RNA (mRNA)-1273 (Moderna) and BNT162b2 (Pfizer-BioNTech). We integrated anti-Spike IgG antibody optical densities with profiles of the waning of antibodies and corresponding probabilities of infection associated with coronavirus endemic transmission. Projecting antibody levels over time given boosting every 6 months, 1, 1.5, 2, or 3 years yielded respective probabilities of fending off infection over a 6-year span of >93%, 75%, 55%, 40%, and 24% (mRNA-1273) and >89%, 69%, 49%, 36%, and 23% (BNT162b2). Delaying the administration of updated boosters has bleak repercussions. It increases the probability of individual infection by SARS-CoV-2, and correspondingly, ongoing disease spread, prevalence, morbidity, hospitalization, and mortality. Instituting regular, population-wide booster vaccination updated to predominant variants has the potential to substantially forestall-and with global, widespread uptake, eliminate-COVID-19. 
    more » « less
  3. ; (, Scientific Reports)
    Abstract Currently, several western countries have more than half of their population fully vaccinated against COVID-19. At the same time, some of them are experiencing a fourth or even a fifth wave of cases, most of them concentrated in sectors of the populations whose vaccination coverage is lower than the average. So, the initial scenario of vaccine prioritization has given way to a new one where achieving herd immunity is the primary concern. Using an age-structured vaccination model with waning immunity, we show that, under a limited supply of vaccines, a vaccination strategy based on minimizing the basic reproduction number allows for the deployment of a number of vaccine doses lower than the one required for maximizing the vaccination coverage. Such minimization is achieved by giving greater protection to those age groups that, for a given social contact pattern, have smaller fractions of susceptible individuals at the endemic equilibrium without vaccination, that is, to those groups that are more vulnerable to infection. 
    more » « less
  4. ; ; ; ; (, Proceedings of the National Academy of Sciences of the United States of America)
    The durability of vaccine-mediated immunity to SARS-CoV-2, the durations to breakthrough infection, and the optimal timings of booster vaccination are crucial knowledge for pandemic response. Here, we applied comparative evolutionary analyses to estimate the durability of immunity and the likelihood of breakthrough infections over time following vaccination by BNT162b2 (Pfizer-BioNTech), mRNA-1273 (Moderna), ChAdOx1 (Oxford-AstraZeneca), and Ad26.COV2.S (Johnson & Johnson/Janssen). We evaluated anti-Spike (S) immunoglobulin G (IgG) antibody levels elicited by each vaccine relative to natural infection. We estimated typical trajectories of waning and corresponding infection probabilities, providing the distribution of times to breakthrough infection for each vaccine under endemic conditions. Peak antibody levels elicited by messenger RNA (mRNA) vaccines mRNA-1273 and BNT1262b2 exceeded that of natural infection and are expected to typically yield more durable protection against breakthrough infections (median 29.6 mo; 5 to 95% quantiles 10.9 mo to 7.9 y) than natural infection (median 21.5 mo; 5 to 95% quantiles 3.5 mo to 7.1 y). Relative to mRNA-1273 and BNT1262b2, viral vector vaccines ChAdOx1 and Ad26.COV2.S exhibit similar peak anti-S IgG antibody responses to that from natural infection and are projected to yield lower, shorter-term protection against breakthrough infection (median 22.4 mo and 5 to 95% quantiles 4.3 mo to 7.2 y; and median 20.5 mo and 5 to 95% quantiles 2.6 mo to 7.0 y; respectively). These results leverage the tools from evolutionary biology to provide a quantitative basis for otherwise unknown parameters that are fundamental to public health policy decision-making. 
    more » « less
  5. ; ; (, Journal of Biological Systems)
    Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which exhibits rich dynamical behavior including supercritical and subcritical Hopf bifurcations among other structures. Here, we extend the bifurcation analyses of the SIRWS model to examine the influence of all parameters on these bifurcation structures. We show that the bistable region, involving both a stable fixed point and a stable limit cycle, exists only for a small region of biologically realistic parameter space. Furthermore, we contrast the SIRWS model with a modified version, where immune boosting may involve the occurrence of a secondary infection. Analysis of this extended model shows that oscillations and bistability, as found in the SIRWS model, depend on strong assumptions about infectivity and recovery rate from secondary infection. Understanding the dynamics of models of waning and boosting immunity is important for accurately assessing epidemiological data. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email