Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo.

This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction number R 0 . For R 0 < 1 , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas for R 0 > 1 , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices for R 0 with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs at R 0 = 1 . Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after 140 - 170 days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population.

Age- and time-dependent prevalence and incidence of hepatitis C virus infection in drug users in France, 2004-2011: model-based estimation from two national cross-sectional serosurveys.

Hepatitis C virus (HCV) infection is a public health issue worldwide. Injecting drug use remains the major mode of transmission in developed countries. Monitoring the HCV transmission dynamic over time is crucial, especially to assess the effect of harm reduction measures in drug users (DU). Our objective was to estimate the prevalence and incidence of HCV infection in DU in France using data from a repeated cross-sectional survey conducted in 2004 and 2011. Age- and time-dependent HCV prevalence was estimated through logistic regression models adjusted for HIV serostatus or injecting practices. HCV incidence was estimated from a mathematical model linking prevalence and incidence. HCV prevalence decreased from 58·2% [95% confidence interval (CI) 49·7-66·8] in 2004 to 43·2% (95% CI 38·8-47·7) in 2011. HCV incidence decreased from 7·9/100 person-years (95% CI 6·4-9·4) in 2004 to 4·4/100 person-years (95% CI 3·3-5·9) in 2011. HCV prevalence and incidence were significantly associated with age, calendar time, HIV serostatus and injecting practices. In 2011, the highest estimated incidence was in active injecting DU (11·2/100 person-years). Given the forthcoming objective of generalizing access to new direct antiviral agents for HCV infection, our results contribute to decision-making and policy development regarding treatment scale-up and disease prevention in the DU population.