Modelling of Waning of Immunity and Reinfection Induced Antibody Boosting of SARS-CoV-2 in Manaus, Brazil

Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages

Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics, however, most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period. This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies. For this purpose, we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period: the first one is an exponential distribution model (EDM), and the other one is a gamma distribution model (GDM); explicit formula of peak time of the EDM is presented via our analytical approach. By data fitting with the COVID-19 (Omicron) epidemic in Spain and Norway, it seems that Spain is more suitable for EDM while Norway is more suitable for GDM. Finally, we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates, and increase of primary course rate (PCR) and booster dose rate (BDR).

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.