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For many infectious diseases, including malaria and COVID-19, the host may experience more than one episode of infection, where reinfection occurs due to waning immunity. In this paper, we propose a new age-structured epidemic model to investigate the dynamics of such diseases with multiple infections. The model is based on a system of partial differential equations that describes the interplay between completely susceptible individuals, temporarily immune individuals, and infected individuals at different stages. The model incorporates both time and age-dependent variables and parameters. We derive the basic reproduction number and conduct rigorous analyses on the equilibrium solutions and their stability properties. Specifically, we study the global asymptotic stability of the disease-free equilibrium and obtain the explicit conditions for the occurrence of a backward bifurcation. Our findings could provide useful insights into the effects of disease prevention and intervention strategies such as vaccination campaigns.
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Epidemic Conditions with Temporary Link Deactivation on a Network SIR Disease Model
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network model in which individuals probabilistically deactivate connections to infected individuals and later reconnect to the same individuals upon recovery. To analyze this network model, a mean field approximation consisting of a system of fourteen ordinary differential equations for the number of nodes and edges is developed. This system of equations is closed using a moment closure approximation for the number of triple links. By analyzing the differential equations, it is shown that, in addition to force of infection and recovery rate, the probability of deactivating edges and the average node degree of the underlying network determine if an epidemic occurs.
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- Award ID(s):
- 1722578
- PAR ID:
- 10354196
- Date Published:
- Journal Name:
- SPORA: A Journal of Biomathematics
- Volume:
- 7
- ISSN:
- 2473-5493
- Page Range / eLocation ID:
- 72-85
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.30707/SPORA7.1.1647885542.976088
