How can risk of COVID-19 transmission be minimised in domiciliary care for older people: development, parameterisation and initial results of a simple mathematical model

Kiss, I.; Blyuss, K.; Kyrychko, Y.; Middleton, J.; Roland, D.; Bertini, L.; Bogen-Johnston, L.; Wood, W.; Sharp, R.; Forder, J.; Cassell, J. A.

This paper proposes and analyses a stochastic model for the spread of an infec- tious disease that is transmitted between clients and care workers in the UK domicil- iary 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 and SEIR-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 quite generic and can be adapted to any particular directly transmitted infectious disease, such as, more recently, COVID-19, provided accurate estimates of disease parameters can be obtained from real data.