Analysis the Dynamics of SIHR Model: Covid-19 Case in Djibouti

The Covid-19 epidemic is an emerging infectious disease of the viral zoonosis type caused by the coronavirus strain SARS-CoV-2, it is classified as a human-to-human communicable disease and is currently a pandemic worldwide. In this paper, we propose conceptual mathematical models of the epidemic dynamics of four compartments. We have collected data from the Djibouti health ministry. We study the positivity, boundedness, existence and uniqueness of the weak solution. Next, we define the Basic reproduction number by the method of the DFE and EEP. Then, we study the local and global stability and the bifurcation analysis of equilibrium to examine its epidemiological relevance. Finally, we analyze the fit of the data in comparison with the result of our mathematical results, to validate the model and estimate the important model parameters and prediction about the disease. We consider the real cases of Djibouti from 15th March to 15th May 2021.

Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

Modeling and investigating malaria P.Falciparum and P.Vivax infections:Application to Djibouti data

Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium parasites.There are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plasmodium Vivax,are the most dangerous.In Djibouti,the two species of Plasmodium are present in different proportions in the infected population:77%of P.Falciparum and 33%of P.Vivax.In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection.We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model(i.e.,existence and stability of various eqiuilibria).Then we use computational approaches to:(a)identify model parameters using real data on malaria infections in Djibouti;(b)illustrate the influence of different estimated parameters on the basic reproduction numbers;(c)perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans,for infections with each of the Plasmodium species.The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti.In addition,sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates.Finally,the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.