Mathematical modeling of infectious disease and designing vaccination law for control of this diseases

In this paper, we propose the concept of partial stability instead of that of global stability to deal with the stability issues of epidemic models. The partial stability is able to provide a more meaningful analysis of the problem since it only focuses on the behavior of some of the variables (infected and infectious) instead of the complete population. It has been shown that the vaccination free SEIR model can still be partially stable even when a globally stability property does not hold, for two types of nonlinear incidence rates. By introducing the concept of partial stability and by designing a control vaccination based on it. Guarantee the eradication of an epidemic disease without requiring the global stability of the epidemic model

A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network

International audienceTo describe failure propagation dynamics in complex dynamical communication networks, we propose an efficient and compartmental standard-exception-failure propagation dynamics model based on the method of modeling disease propagation in social networks. Mathematical formulas are derived and differential equations are solved to analyze the equilibrium of the propagation dynamics. Stability is evaluated in terms of the balance factor G and it is shown that equilibrium where the number of nodes in different states does not change, is globally asymptotically stable if G≥1. The theoretical results derived are verified by numerical simulations. We also investigate the effect of some network parameters, e.g. node density and node movement speed, on the failure propagation dynamics in complex dynamical communication networks to gain insights for effective measures of control of the scale and duration of the failure propagation in complex dynamical communication networks

Mitigating Epidemics through Mobile Micro-measures

Epidemics of infectious diseases are among the largest threats to the quality of life and the economic and social well-being of developing countries. The arsenal of measures against such epidemics is well-established, but costly and insufficient to mitigate their impact. In this paper, we argue that mobile technology adds a powerful weapon to this arsenal, because (a) mobile devices endow us with the unprecedented ability to measure and model the detailed behavioral patterns of the affected population, and (b) they enable the delivery of personalized behavioral recommendations to individuals in real time. We combine these two ideas and propose several strategies to generate such recommendations from mobility patterns. The goal of each strategy is a large reduction in infections, with a small impact on the normal course of daily life. We evaluate these strategies over the Orange D4D dataset and show the benefit of mobile micro-measures, even if only a fraction of the population participates. These preliminary results demonstrate the potential of mobile technology to complement other measures like vaccination and quarantines against disease epidemics.Comment: Presented at NetMob 2013, Bosto

Analysis of SIR epidemic models with sociological phenomenon

We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of $R_0$ to changes in sociological parameter values

Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results

Modeling immune response and its effect on infectious disease outbreak dynamics

This article presents a model that incorporates individuals' immune responses to further examine the role of the collective immune response of individuals in a population during an infectious outbreak