Related papers: A vector-host epidemic model with spatial structur…
An important issue in theoretical epidemiology is the epidemic threshold phenomenon, which specify the conditions for an epidemic to grow or die out. In standard (mean-field-like) compartmental models the concept of the basic reproductive…
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…
A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases,…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
In this paper, we develop a method to estimate the infection-rate of a disease, over a region, as a field that varies in space and time. To do so, we use time-series of case-counts of symptomatic patients as observed in the areal units that…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
A mathematical model of Zika virus transmission incorporating human movement between rural areas and nearby forests is presented to investigate the role of human movement in the spread of Zika virus infections in human and mosquito…
Multiple instances of Zika virus epidemic have been reported around the world in the last two decades, turning the related illness into an international concern. In this context the use of mathematical models for epidemics is of great…
Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence system are overwhelming against advanced propagation of the disease. News are becoming more effortlessly…
Over 50% of the world population is at risk of mosquito-borne diseases. Female Ae. aegypti mosquito species transmit Zika, Dengue, and Chikungunya. The spread of these diseases correlate positively with the vector population, and this…
For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are…
Population heterogeneity is a key factor in epidemic dynamics, influencing both transmission and final epidemic size. While heterogeneity is often modelled through age structure, spatial location, or contact patterns, differences in host…
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…
Understanding the dynamics of infectious disease spread in a heterogeneous population is an important factor in designing control strategies. Here, we develop a novel tensor-driven multi-compartment version of the classic…
We consider a model for an influenza-like disease, in which, between seasons, the virus makes a random genetic drift $\delta$, (reducing immunity by the factor $\delta$) and obtains a new random transmissibility $\tau$ (closely related to…
In this work we propose a measure-valued stochastic process representing the dynamics of a virus population, structured by phenotypic traits and geographical space, and where viruses are transported between spatial locations by mechanical…
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
We propose a nonlocal epidemic model whose spatial domain evolves over time and is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front of epidemic. It is assumed that the agents can cross the fixed boundary $x=0$, but…
Deterministic models are developed for the spatial spread of epidemic diseases in geographical settings. The models are focused on outbreaks that arise from a small number of infected hosts imported into sub-regions of the geographical…