Age-Structured Model for COVID-19: Effectiveness of Social Distancing and Contact Reduction

Abstract Background : Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2. The disease has spread to almost every country in the world. Kenya reported its first case on 13th of March 2020. From 16th March 2020, the country instituted various social distancing strategies to reduce the transmission and flatten the epidemic curve. These strategies include school closure, dusk-to-dawn curfew, and travel restriction across counties, especially Nairobi, Mombasa and Kwale. An age-structured compartmental model was developed to assess the impact of non-pharmaceutical interventions on severity of infections, hospital demands and deaths. Methods : The population is divided into four age-groups and for each age-group there are seven compartments, namely: susceptible , exposed, asymptomatic, mild, severe, critical, death and recovered. The contact matrices between the different ages are integrated into an age-structured deterministic model via the force of infection. This model is represented by ordinary differential equations and solved using Runge–Kutta methods, with suitable model parameters. Simulation results for the unmitigated and mitigated scenarios were depicted, for the different age-groups. Results : The 45% reduction in contacts for 60-days period resulted to between 11.5-13% reduction of infections severity and deaths, while for the 190-days period yielded between 18.8-22.7% reduction. The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation, which happened just a month after mitigation were relaxed. Low numbers of cases in children under 15 years was attributed to low susceptibility of persons in this age-group. High numbers of cases are reported in the 15-29 years and 30-59 years age bands since these individuals have wider interaction spheres, and they form a significant percentage of Kenya population. Conclusion : Two mitigation periods, considered in the study, resulted to reductions in severe and critical cases, attack rates, hospital and ICU bed demands, as well as deaths, with the 190-days period giving higher reductions. The study revealed the age-dependency of the key health outputs.