Walid Aribi

COVID-19 remains a major threat to the world since its emergence in December 2019, especially the lack of identification of a specific treatment, as scientific researchers continue to seek a better understanding of the epidemiological cycle and dynamics of the virus. Mathematical modeling of the COVID-19 disease can provide better insight into the complex dynamics of the virus and define preventive measures that can be used to contain the spread of the disease. In this research article, we propose a model describes the epidemic dynamics of Covid-19 in a population after vaccine deployment, is an extension of the standard SEAIR model incorporating temporary protection vaccine compartment. An optimal control problem is formulated with the aim of minimizing the number of infected individuals while considering intervention costs and the constraints of the total and maximum daily vaccineadministration. We use the penalty method to approximate this constrained optimization problem and derive an optimality system that characterizes the optimal control. Finally, we carry out numerical simulations using reported data on COVID-19 infections and vaccination in France and in Tunisia, compare these two countries in the face of the pandemic.

Background: The epidemiological pattern of hepatitis A infection has shown dynamic changes in many parts of the world due to improved socio-economic conditions and the accumulation of seronegative subjects, which leads to possible outbreaks and increased morbidity rate. In Tunisia, the epidemiological status of hepatits A virus is currently unknown. However, over the past years higher numbers of symptomatic hepatitis A virus infection in school attendants and several outbreaks were reported to the Ministry of Health, especially from regions with the lowest socio-economic levels in the country. The aim of this study was to investigate the current seroprevalence of hepatitis A virus antibodies in central-west Tunisia and assess the impact of hepatitis A virus vaccination on hepatitis A epidemiology. Methods: Serum samples from 1379 individuals, aged 5–75 years, were screened for hepatitis A virus antibodies. Adjusted seroprevalence, incidence and force of infection parameters were estimated by a linear age structured SEIR (Susceptible-Exposed-Infectious-Recovered) compartmental model. A vaccine model was then constructed to assess the impact on hepatitis A virus epidemiology of 3 scenarios of vaccination strategies: one dose at 12-months of age, one dose at 6-years and one dose at 12-months and another at 6-years of age during 6 years. Results: A rapid increase in anti-hepatitis A virus seroprevalence was noted during infancy and adolescence: 47% of subjects under 10-years-old are infected; the prevalence increases to 77% at 15-years and reaches 97% in subjects aged 30-years. The force of infection is highest between 10 and 30-years of age and the incidence declines with increasing age. The vaccine model showed that the 3-scenarios lead to a significant reduction of the fraction of susceptibles. The two doses scenario gives the best results. Single-dose vaccination at 6-years of age provides more rapid decrease of disease burden in school-aged children, as compared to single-dose vaccination at 12-months, but keeps with a non-negligible fraction of susceptibles among children < 6-years. Conclusions: Our study confirms the epidemiological switch from high to intermediate endemicity of hepatitis A virus in Tunisia and provides models that may help undertake best decisions in terms of vaccinations strategies.