The COVID-19 pandemic, caused by the SARS-CoV-2 virus, presented unprecedented challenges globally. Many countries implemented non-pharmaceutical interventions (NPIs) like lockdowns and social distancing to control the spread. The effectiveness of these NPIs depends heavily on understanding disease dynamics, and mathematical models are crucial for forecasting. This study focuses on Ukraine, a large European country, to develop a detailed mathematical model of COVID-19 transmission, leveraging the latest data on clinical features of the disease. The model's accuracy is enhanced by incorporating age-stratified parameters and age- and location-specific contact matrices to represent population interactions. The goal is to provide accurate short-term forecasts and assess the impact of various lockdown strategies.

Numerous studies have used mathematical models to analyze the effectiveness of social distancing measures in reducing COVID-19 spread (citations 3-9). These models have highlighted the importance of understanding asymptomatic transmission (citations 10, 11), age-related disease severity (citations 12, 13), incubation periods (citation 14), and the role of viral load (citation 15). Prior work by Blyuss and Kyrychko (citation 16) and Brovchenko (citation 17) on COVID-19 dynamics, respectively in the UK and Ukraine, laid the groundwork for the current study. The study also draws on the work of Davies et al. (citation 18) regarding the modeling of different types of clinical progression of COVID-19 and the need for hospitalization.

The researchers developed an age-structured SEIR (Susceptible, Exposed, Infected, Recovered) compartmental model. The model incorporates several modifications: asymptomatic carriers, different clinical progression pathways (mild, severe, death), hospitalization, and immunity after recovery. The model divides the population into sixteen 5-year age groups. A contact matrix (equation 1) incorporates daily contacts in school, work, home, and other settings (a1, a2, a3, a4 coefficients). The gamma distribution was used to approximate the distributions of incubation time (Tinc, K1), infectious period (Tinf, K2), hospital recovery period (Tsev, K3), and time to death (Tdeath, K4) (Figure 2). Parameter values, including age-specific proportions of asymptomatic cases, hospitalization rates, and mortality rates, were obtained from the Public Health Center of the Ministry of Health of Ukraine (Table 1). The model uses age-specific contact matrices (Figure 8) from a POLYMOD study adapted for Ukraine (citation 43). The model's dynamics were simulated by adjusting the coefficients (a1-a4) in the contact matrix to reflect the various lockdown measures implemented in Ukraine at different times. A seven-day moving average of reported cases was used to estimate the disease transmission rate (β), allowing for a close tracking of changes associated with NPIs.

The model accurately predicts the short-term dynamics of COVID-19 cases and deaths in Ukraine (Figure 3). A plateau-like phase was observed from mid-April to the end of May 2020, coinciding with stringent lockdown measures. The subsequent easing of restrictions led to a significant increase in cases and deaths. The age distribution of cases and deaths stabilized by mid-April (Figure 4). A notable finding is the high proportion of deaths in the 50-70 age group (nearly 50%), possibly due to lower life expectancy and high rates of comorbidities. Longer-term forecasts (Figure 5) indicate that a 10% increase in the transmission rate, coupled with the planned reopening of schools, could reverse the downward trend and lead to a resurgence of cases in the late autumn. A 20% increase results in a substantial surge in cases and deaths. Simulation of various lockdown scenarios (Figure 6) reveals that reducing work contacts is the most effective strategy for minimizing both cases and deaths, more so than reducing school contacts or shielding the elderly. This is likely due to the significant contribution of working-age individuals to disease transmission.

The findings highlight the importance of timely and effective NPIs in controlling COVID-19 spread. The model's accurate short-term predictions underscore the value of incorporating realistic parameters and age-structured contact patterns. The significant death rate in the 50-70 age group emphasizes the need for targeted interventions to protect this vulnerable population. The study's findings strongly support policies promoting working from home and reducing crowded public transport to minimize disease burden. The model’s relatively good performance in forecasting COVID-19 cases and deaths in Ukraine during the first half of October 2020 (comparison with actual data made at the end of the paper) further supports the robustness of the model. The discrepancy between simulated and observed age distribution can be due to factors like inaccuracies in mixing matrices, regional variations, and data reporting issues.

This study provides a robust mathematical model for forecasting COVID-19 dynamics in Ukraine. The results underscore the critical role of age-structured modeling and the significant impact of different NPI strategies. Reducing work-related contacts appears to be the most effective approach. Future research could focus on improving the accuracy of contact matrices using detailed surveys, incorporating regional variations, and modeling the effects of misinformation and public awareness campaigns.

The model relies on the accuracy and timeliness of reported case and death data, which may be subject to delays or underreporting. The contact matrices used may not perfectly represent actual mixing patterns in the Ukrainian population. Regional variations in population structure and contact patterns are not fully captured in this pan-Ukrainian model. The absence of data on the distribution of infectious period (Tinf) and the use of an earlier estimation based on similar studies may affect model accuracy.