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We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R ∗ >1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R ∗ <1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R ∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R ∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R ∗ appearing in this model are both responsible for the existence of endemic states., Competing Interests: Declaration of competing interest The authors of the manuscript José Manuel Islas, Ruth Corona-Moreno and Jorge X. Velasco-Hernández, declare that they have NO affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript., (Copyright © 2024 Elsevier Inc. All rights reserved.)

In this paper we address the problem of estimating the parameters of Markov jump processes modeling epidemics and introduce a novel method to conduct inference when data consists on partial observations in one of the state variables. We take the classical stochastic SIR model as a case study. Using the inverse-size expansion of van Kampen we obtain approximations for the first and second moments of the state variables. These approximate moments are in turn matched to the moments of an inputed Generic Discrete distribution aimed at generating an approximate likelihood that is valid both for low count or high count data. We conduct a full Bayesian inference using informative priors. Estimations and predictions are obtained both in a synthetic data scenario and in two Dengue fever case studies., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Simple patch-occupancy models of competitive metacommunities have shown that coexistence is possible as long as there is a competition-colonization tradeoff such as that of superior competitors and dispersers. In this paper, we present a model of competition between three species in a dynamic landscape, where patches are being created and destroyed at a different rate. In our model, species interact according to a linear non-transitive hierarchy, such that species Y(3) outcompetes and can invade patches occupied by species Y(2) and this species in turn can outcompete and invade patches occupied by the inferior competitor Y(1). In this hierarchy, inferior competitors cannot invade patches of species with higher competitive ability. Analytical results show that there are regions in the parameter space where coexistence can occur, as well as regions where each of the species exists in isolation depending on species' life-history traits associated with their colonization abilities and extinction proneness as well as with the dynamics of habitat patches. In our model, the condition for coexistence depends explicitly on patch dynamics, which in turn modulate the limiting similarity for species coexistence. Coexistence in metacommunities inhabiting dynamic landscapes although possible is harder to attain than in static ones.