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Crohn's disease is an inflammatory bowel disease (IBD) that is not well understood. In particular, unlike other IBDs, the inflamed parts of the intestine compromise deep layers of the tissue and are not continuous but separated and…
In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI),…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…
We study a dynamics of the epidemiological infection spreading at different values of the risk factor $\beta$ (a control parameter) with the using of dynamic Monte Carlo approach (DMC). In our toy model, the infection transmits due to…
This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…
We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are…
The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative…
We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19…
Transmission dynamics of infectious diseases are often studied using compartmental mathematical models, which are commonly represented as systems of autonomous ordinary differential equations. A key step in the analysis of such models is to…
Much traditional statistical modelling assumes that the outcome variables of interest are independent of each other when conditioned on the explanatory variables. This assumption is strongly violated in the case of infectious diseases,…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
As the outbreak of COVID-19 enters its third year, we have now enough data to analyse the behavior of the pandemic with mathematical models over a long period of time. The pandemic alternates periods of high and low infections, in a way…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…
Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission…
We establish some properties of a within host mathematical model of malaria proposed by Recker et al which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria…
We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
Molecular communication between biological entities is a new paradigm in communications. Recently, we studied molecular communication between two nodes formed from synthetic bacteria. Due to high randomness in behavior of bacteria, we used…
Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based on environmental…
We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…