COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY

Details

• Alternative Title:
  Discrete Continuous Dyn Syst Ser B
• Personal Author:
  Feng, Zhilan ; Han, Qing ; Qiu, Zhipeng ; Hill, Andrew N. ; Glasser, John W.
• Description:
  For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.
• Subjects:
  Age-structured Epidemiological Model Article Multiple Infections Partial Immunity Reproduction Numbers
• Source:
  Discrete Continuous Dyn Syst Ser B. 21(2):399-415.
• Pubmed ID:
  29249910
• Pubmed Central ID:
  PMC5730097
• Document Type:
  Journal Article
• Funding:
  CC999999/Intramural CDC HHS/United States
• Volume:
  21
• Issue:
  2
• Collection(s):
  CDC Public Access
• Main Document Checksum:
  urn:sha256:2e0ab6507de0cc87b53380487b19c510fa7be8308291b736a10bc8a6260998db
• Download URL:
  https://stacks.cdc.gov/view/cdc/50712/cdc_50712_DS1.pdf
• File Type:
  [PDF - 1.31 MB ]