ABSTRACT
This paper proposes and analyses a stochastic model for the spread of an infectious disease transmitted between clients and care workers in the UK domiciliary (home) care setting. Interactions between clients and care workers are modelled using specially generated networks, with network parameters reflecting realistic patterns of care needs and visit allocation. These networks are then used to simulate a susceptible-exposed-infected-recovered/dead (SEIR/D)-type epidemic dynamics with different numbers of infectious and recovery stages. The results indicate that with the same overall capacity provided by care workers, the minimum peak proportion of infection and the smallest overall size of infection are achieved for the highest proportion of overlap between visit allocation, i.e. when care workers have the highest chances of being allocated a visit to the same client they have visited before. An intuitive explanation of this is that while providing the required care coverage, maximising overlap in visit allocation reduces the possibility of an infectious care worker inadvertently spreading the infection to other clients. The model is generic and can be adapted to any directly transmitted infectious disease, such as, more recently, corona virus disease 2019, provided accurate estimates of disease parameters can be obtained from real data.
ABSTRACT
In this paper we develop an SEIR-type model of COVID-19, with account for two particular aspects: non-exponential distribution of incubation and recovery periods, as well as age structure of the population. For the mean-field model, which does not distinguish between different age groups, we demonstrate that including a more realistic Gamma distribution of incubation and recovery periods may not have an effect on the total number of deaths and the overall size of an epidemic, but it has a major effect in terms of increasing the peak numbers of infected and critical care cases, as well as on changing the timescales of an epidemic, both in terms of time to reach the peak, and the overall duration of an outbreak. In order to obtain more accurate estimates of disease progression and investigate different strategies for introducing and lifting the lockdown, we have also considered an age-structured version of the model, which has allowed us to include more accurate data on age-specific rates of hospitalisation and COVID-19 related mortality. Applying this model to three comparable neighbouring regions in the UK has delivered some fascinating insights regarding the effect of lockdown in regions with different population structure. We have discovered that for a fixed lockdown duration, the timing of its start is very important in the sense that the second epidemic wave after lifting the lockdown can be significantly smaller or larger depending on the specific population structure. Also, the later the fixed-duration lockdown is introduced, the smaller is the resulting final number of deaths at the end of the outbreak. When the lockdown is introduced simultaneously for all regions, increasing lockdown duration postpones and slightly reduces the epidemic peak, though without noticeable differences in peak magnitude between different lockdown durations.