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We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered {\it at-risk} is modeled using a strictly decreasing general…
\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are…
We propose and study a fully efficient method to estimate associations of an exposure with disease incidence when both, incident cases and prevalent cases, i.e. individuals who were diagnosed with the disease at some prior time point and…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
In this paper, the main purpose is to explore an SIRS epidemic model with a general nonlinear incidence rate $f(I)S=\beta I(1+\upsilon I^{k-1})S$ ($k>0$). We analyzed the existence and stability of equilibria of the epidemic model. Local…
We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…
The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2008, Tournoud and Ecochard first proposed a mechanistic formulation of cure…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical…
We study the dynamics of a SIR epidemic model with nonlinear incidence rate, vertical transmission vaccination for the newborns and the capacity of treatment, that takes into account the limitedness of the medical resources and the…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…
We extend the continuity-based framework to Regression Discontinuity Designs (RDDs) to identify and estimate causal effects under interference when units are connected through a network. Assignment to an "effective treatment," combining the…
A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium…
This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an…
We consider a causal inference model in which individuals interact in a social network and they may not comply with the assigned treatments. In particular, we suppose that the form of network interference is unknown to researchers. To…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…