We propose a mathematical model describing the dynamics of hematopoietic stem cell population. The method characteristics reduces age-structured to system differential equations with state-dependent delay. A detailed stability analysis is performed. sufficient condition for global asymptotic trivial steady state obtained using Lyapunov–Razumikhin function. unique positive shown appear through transcritical bifurcation state. behavior, study first order exponential polynomial characteristic...

We propose a mathematical model describing the dynamics of hepatitis B or C virus infection. The method characteristics reduces age-structured to system differential equations with distributed delay. is rigorously analyzed, and detailed stability analysis performed. model, consisting two mutually exclusive compartments representing interaction in liver blood, has locally asymptotically stable disease-free equilibrium (DFE) whenever certain epidemiological threshold, known as basic...

Genital Herpes, which is caused by Herpes Simplex Virus-1 or -2 (HSV-1, -2, predominantly HSV-2) a sexually transmitted infection (STI) that causes chronic latent with outbreak episodes linked to transmission. Antiviral therapies are effective in reducing viral shedding during these episodes, but ineffective as whole since many outbreaks asymptomatic have mild symptoms. Thus, the development of vaccine for genital herpes needed control this disease. The question how implement such program an...

Consider the functional differential equation (FDE)$\dot{x}(t)=f(x_t)$ with $f$ defined on an open subset of space$C^1=C^1([-h,0],\R^n)$. Under mild smoothness assumptions, which aredesigned for application to equations withstate-dependent delays, FDE generates a semiflow asubmanifold $C^1$ continuously differentiable time-$t$-maps.We show that at stationary point localcenter-stable manifolds exist. The proof usesresults Chen, Hale and Tan Krisztin about invariantmanifolds time-$t$-maps...

The paper addresses the computation of elements double Hopf bifurcation for retarded functional differential equations (FDEs) with parameters. We present an efficient method computing, simultaneously, coefficients center manifolds and normal forms, in terms original FDEs, associated singularity up to arbitrary order. Finally, we apply our results a nonlinear model periodic delay. This shows applicability methodology study delay models arising either natural or technological problems.

Abstract Public health control strategies, such as lockdown, seem to be effective in reducing the spread of pandemic, but are ineffective a whole since lockdown is responsible global economic crisis and badly lived by majority children adults who have developed mental disorders familial problems well. Thus, development vaccine against COVID-19 needed this disease. We discrete age-structured model followed Moroccan vaccination program assess impact booster targeting COVID-19. Using derived...

Abstract Background Since the appearance of first case COVID-19 in Morocco, cumulative number reported infectious cases continues to increase and, consequently, government imposed containment measure within country. Our aim is predict impact compulsory on spread. Earlier knowledge epidemic characteristics transmission related Morocco will be great interest establish an optimal plan-of-action control epidemic. Method Using a Susceptible-Asymptomatic-Infectious model and data confirmed from...

In this survey, we collect a few results scatted in the literature covering advances systems of periodic delay differential equations including both modeling and theory. We will present (almost) most oldest recent contributions made for subject.

The breast milk of HIV infected women contains virus particles, therefore children can become through breastfeeding. We develop a mathematical epidemiological model infection in infants, and that represents an infant/child as series exposures, by incorporating within-host dynamics the individuals exposed to show repeated exposures via breastfeeding cause bi-stability and, subsequently, persistence even when basic reproduction number R0 is less than unity. This feature model, due backward...

Dynamic behavior investigations of infectious disease models are central to improve our understanding emerging characteristics model states interaction. Here, we consider a Susceptible-Infected (SI) with general state-dependent delay, which covers an immuno-epidemiological pathogen transmission, developed in early study, using threshold delay examine the effects multiple exposures pathogen. The analysis previous work showed appearance forward as well backward bifurcations endemic equilibria...

The main focus of this chapter is on public health control strategies which are currently the way to mitigate COVID-19 pandemic. We introduce and compare compartmental models increasing complexity for transmission describe dynamics disease spread. begin by considering an SEAIR model including basic characteristics related COVID-19. Next, we shall pay attention age-structure modeling emphasis role age-group individuals A Model with constant delay also formulated show impact latency period...