Browsing by Subject "SIR-malli"

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  • Blom, Patrick (Helsingin yliopisto, 2020)
    In times of epidemics, few people continue living as usual and instead often change their behaviour in light of the new situation. Usually the change in behaviour is taken to be preventive measures aimed the reduce the probability of infectious contact between susceptibles and infected. This thesis considers a different scenario, where susceptibles, once gaining awareness of the disease, begin to consider vaccination against the disease. The basic SIR-model is modified to include awareness of the epidemic or the possibility thereof, that inspires individuals to vaccinate themselves. The awareness is spread either from a constant source outside the population or through contacts between unaware individuals and either the infected or individuals already aware of the disease. The equilibria of these models and the conditions for their stability are established. All three models significantly reductions to the final size of the epidemic. In case of awareness spread being dependent on the size of the infected population, under some conditions the introducing vaccinations can destabilize the endemic equilibrium and lead to oscillations. Constant and aware-dependent awareness models also have disease-free equilibria, which can be stable and prevent a major epidemic from happening if the spread of awareness is strong enough. Lattice-model analogues of the constant and aware-dependent awareness models, where individuals are connected to a limited number of other individuals, are also established along with their equilibria. Also in this case, the disease-free equilibria of the two models can be stabilised with an effective spread of awareness.