Stability and thresholds in some age-structured epidemics.

*(English)*Zbl 0686.92014
Mathematical approaches to problems in resource management and epidemiology, Proc. Conf., Ithaca/NY (USA) 1987, Lect. Notes Biomath. 81, 124-141 (1989).

Summary: [For the entire collection see Zbl 0682.00021.]

Age-structured models for diseases that can be transmitted both horizontally and vertically are derived and analyzed. The relation between these models and the catalytic curve models of epidemics is explicitly given. The possibility of using the catalytic curve to deduce information about the age-dependent contact rate and to identify the presence of vertical transmission is demonstrated. For certain age- dependent forms of the force of infection terms, explicit endemic threshold criteria are derived, and the stability of the steady states is determined.

Age-structured models for diseases that can be transmitted both horizontally and vertically are derived and analyzed. The relation between these models and the catalytic curve models of epidemics is explicitly given. The possibility of using the catalytic curve to deduce information about the age-dependent contact rate and to identify the presence of vertical transmission is demonstrated. For certain age- dependent forms of the force of infection terms, explicit endemic threshold criteria are derived, and the stability of the steady states is determined.

##### MSC:

92D25 | Population dynamics (general) |

35Q99 | Partial differential equations of mathematical physics and other areas of application |