Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate.
Global existence and asymptotic behaviour for a degenerate diffusive SEIR model.
Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment
This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.
Global stability analysis and control of leptospirosis
The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction...
Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and normated function k defined...
Hopf bifurcation for a model of HIV infection of T cells with virus released delay.
Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics.
Importance of brood maintenance terms in simple models of the honeybee - Varroa destructor - acute bee paralysis virus complex.
Individual-based lattice model for spatial spread of epidemics.
Influenza Transmission in Preschools: Modulation by contact landscapes and interventions
Epidemiologic data suggest that schools and daycare facilities likely play a major role in the dissemination of influenza. Pathogen transmission within such small, inhomogenously mixed populations is difficult to model using traditional approaches. We developed simulation based mathematical tool to investigate the effects of social contact networks on pathogen dissemination in a setting analogous to a daycare center or grade school. Here we show...
Když se matematika potká s biologií: matematická epidemiologie
Středověká morová epidemie způsobila smrt asi 17-22 % světové populace, z toho asi 30-60 % evropské populace, a trvalo zhruba 200 let, než se světová populace vrátila na svou původní úroveň. Epidemie dnes často zmiňované španělské chřipky v letech 1918-1920 vedla ke smrti přibližně 3-5 % světové populace. Svědky méně závažných, avšak stále dramatických epidemií jsme i v současnosti. Pandemie těžkého akutního respiračního syndromu (SARS) mezi roky 2002 a 2004, pandemie prasečí chřipky způsobené kmenem...
Kermack-McKendrick epidemics vaccinated
This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...
Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models
Mathematical model of dengue disease transmission with severe DHF compartment.
Mathematical modeling of antigenicity for HIV dynamics
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...
Media/psychological impact on multiple outbreaks of emerging infectious diseases.
Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study
Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour...
Modeling Adaptive Behavior in Influenza Transmission
Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical...
Modeling HIV epidemic under contact tracing -- the Cuban case.
Modelling the Spread of Infectious Diseases in Complex Metapopulations
Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially,...