Related papers: A vector-host epidemic model with spatial structur…
In this paper, we introduce a modified epidemic model on regular and scale-free networks respectively. We consider the birth rate $\delta$, cure rate $\gamma$, infection rate $\lambda$, $\alpha$ from the infectious disease, and death rate…
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…
Zika virus (ZIKV), a disease spread primarily through the Aedes aegypti mosquito, was identified in Brazil in 2015 and was declared a global health emergency by the World Health Organization (WHO). Epidemiologists often use common…
In this article we consider a microscopic model for host-vector disease transmission based on configuration space analysis. Using Vlasov scaling we obtain the corresponding mesoscopic (kinetic) equations, describing the density of…
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master…
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not…
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the…
We propose a model of the immunity to a cyclical epidemic disease taking account not only of seasonal boosts during the infectious season, but also of residual immunity remaining from one season to the next. The focus is on the exponential…
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
This paper aims to explore the temporal-spatial spreading and asymptotic behaviors of West Nile virus by a reaction-advection-diffusion system with free boundaries, especially considering the impact of advection term on the extinction and…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…
We present a mathematical model for within host viral infections that incorporates the Crowley Martin functional response, focusing on the dynamics influenced by periodic effects. This study establishes key properties of the model,…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of…
This paper analyzes a simplified model of viral infection and evolution using the 'grand canonical ensemble' and formalisms from statistical mechanics and thermodynamics to enumerate all possible viruses and to derive thermodynamic…
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally…