| Abstract: |
| We study the dynamics of compartmental disease models with time-dependent parameters. As a particular disease, we consider bacterial meningitis with two age classes and seasonal exacerbations. The time-dependent transmission parameters may represent the outbreak of meningitis cases after the annual pilgrimage period or uncontrolled inflows of irregular immigrants. We consider periodic functions in the analysis of the parameters, as well as more general non-periodic transmission processes. We derive conditions under which the long-time average values of transmission functions can be used as a stability marker of equilibria. Furthermore, we interpret the basic reproduction number in the case of time-dependent transmission functions. |
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