We developed an epidemic model with disease awareness and variable susceptibility, consisting of a two-dimensional, nonlocal, transport equation. From this model, we deduced a 3D ordinary differential equation (ODE) model, which is reminiscent of (but not reducible to) more traditional susceptible-infectious-susceptible (SIS)-type models, where the dynamical variables are the infected population proportion, the mean awareness of the population, and the mean susceptibility to reinfection. We show that a reproduction number $ R_0 $ exists whose threshold value determines the stability of the disease-free equilibrium, alongside the existence of an endemic one. We deduced conditions on the model parameters and ensured the stability and uniqueness of the endemic equilibrium. The transport equation was studied, and we showed some numerical experiments. Our results suggest that disease awareness dynamics can have a major role in epidemiological outcomes: we showed that even for high $ R_0 $, the infection prevalence could be made as small as desired, as long as the awareness decay was small. On the other hand, numerical evidence suggested that the relation between epidemiological outcomes and awareness levels was not straightforward, in the sense that sustained high awareness may not always lead to better outcomes, as compared to time-limited awareness peaks in response to outbreaks.
Citation: Paulo Amorim, Alessandro Margheri, Carlota Rebelo. Modeling disease awareness and variable susceptibility with a structured epidemic model[J]. Networks and Heterogeneous Media, 2024, 19(1): 262-290. doi: 10.3934/nhm.2024012
We developed an epidemic model with disease awareness and variable susceptibility, consisting of a two-dimensional, nonlocal, transport equation. From this model, we deduced a 3D ordinary differential equation (ODE) model, which is reminiscent of (but not reducible to) more traditional susceptible-infectious-susceptible (SIS)-type models, where the dynamical variables are the infected population proportion, the mean awareness of the population, and the mean susceptibility to reinfection. We show that a reproduction number $ R_0 $ exists whose threshold value determines the stability of the disease-free equilibrium, alongside the existence of an endemic one. We deduced conditions on the model parameters and ensured the stability and uniqueness of the endemic equilibrium. The transport equation was studied, and we showed some numerical experiments. Our results suggest that disease awareness dynamics can have a major role in epidemiological outcomes: we showed that even for high $ R_0 $, the infection prevalence could be made as small as desired, as long as the awareness decay was small. On the other hand, numerical evidence suggested that the relation between epidemiological outcomes and awareness levels was not straightforward, in the sense that sustained high awareness may not always lead to better outcomes, as compared to time-limited awareness peaks in response to outbreaks.
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Paulo Amorim, Alessandro Margheri, Carlota Rebelo. Modeling disease awareness and variable susceptibility with a structured epidemic model[J]. Networks and Heterogeneous Media, 2024, 19(1): 262-290. doi: 10.3934/nhm.2024012
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