Migration rate estimation in an epidemic network

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metapopulation model over a network. Our model postulates a general contact rate that represents a local measure of several factors: the population size of infected hosts that arrive at a given location as a function of total population size, the current incidence at neighboring locations, and the connectivity of the network where the disease spreads. This parameter can be interpreted as an indicator of outbreak risk at a given location. This parameter is tied to the fraction of individuals that move across boundaries (migration). To illustrate our model capabilities, we estimate from epidemic Dengue data in Mexico the dynamics of migration at a regional scale incorporating climate variability represented by an index based on precipitation data.

Threshold parameters and metapopulation persistence

A method is presented to estimate the minimum viable metapopulation size based on the basic reproductive number R(0) and the expected time to extinction tau(E) for epidemiological models. We exemplify our approach with two simple deterministic metapopulation models of the patch occupancy type and then proceed to stochastic versions that permit the estimation of the minimum viable metapopulation size.

Porosity and tortuosity relations as revealed by a mathematical model of biofilm structure

A biofilm is assumed to be submerged in a fluid with given viscosity and low Reynolds number. The interaction between fluid and bacteria is modeled through streamlines. We use finite-difference and boundary element numerical schemes to predict streamlines within the biofilm. The results show that this approach can provide information about prior distribution and geometry of the biofilm structure. Theoretical values of porosity and tortuosity are computed and compared with published data.

A simple vaccination model with multiple endemic states

A simple two-dimensional SIS model with vaccination exhibits a backward bifurcation for some parameter values. A two-population version of the model leads to the consideration of vaccination policies in paired border towns. The results of our mathematical analysis indicate that a vaccination campaign φ meant to reduce a disease's reproduction number R(φ) below one may fail to control the disease. If the aim is to prevent an epidemic outbreak, a large initial number of infective persons can cause a high endemicity level to arise rather suddenly even if the vaccine-reduced reproduction number is below threshold. If the aim is to eradicate an already established disease, bringing the vaccine-reduced reproduction number below one may not be sufficient to do so. The complete bifurcation analysis of the model in terms of the vaccine-reduced reproduction number is given, and some extensions are considered.

On the Relationship Between Evolution of Virulence and Host Demography

The effects of density-dependence on the evolution of virulence in super-infection models is the theme of this paper. The qualitative dynamics of three host-pathogen systems are studied numerically in a virulence-superinfection parameter landscape. It is shown numerically that pathogen's competitive exclusion coexistence and host population extinction depend heavily of the population dynamics of the host population. Reported patterns of diversity found using models without demography, are insufficient to account for the coevolutionary dynamics under defined selective pressures. Specifically, virulence and superinfection in the presence of a variable host population give rise to threshold values that divide (as switches) the regions of coexistence and competitive exclusion. Tight coevolution on a variable host population may occur within regions of parameter space that are not connected. We present our numerical results using a simple host-disease system where a homogeneous host population is invaded by two competing pathogen strains (partial analytical results will be published elsewhere).Copyright 1998 Academic Press Limited

Competitive exclusion in a vector-host model for the dengue fever

We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state ('saddle' point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates.

Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease

This paper studies models for the sexual transmission of HIV/AIDS that incorporate changes in behaviour and the effects associated with HIV treatment. The recruitment rate into the core is assumed to be a function of the prevalence of the disease within the core, and it may trigger the existence of periodic solutions through Hopf bifurcations, provided that there is at least a weak demographic interaction with the noncore. The recruitment function is set up for two cases: dependence on the total proportion of infectious individuals and dependence on the proportion of treated infectious individuals only. In the general model, numerical evidence suggests that both cases may produce periodic solutions when the perception of the risk of joining the core group is sufficiently high. Two limiting cases are also studied: when the growth rate of the core and noncore groups are essentially the same, and when treatment has no effect on the transmission rate of infected individuals.

A model for Chagas disease involving transmission by vectors and blood transfusion

Models on the population dynamics of Chagas disease are discussed. The effects of vector and blood transfusion transmission are considered and epidemiological data is provided to support model assumptions. Also, the role of density-dependence on the population dynamics of the vector population is explored as well as the existence of non-reproductive insect stages involved in the transmission process. When density dependent effects are neglected, there is a non-oscillatory approach to the endemic equilibrium (local asymptotic stability). When density-dependence effects and vector stage-structure are introduced, limit cycle solutions may be obtained. Results are compared to available field data.

An epidemiological model for the dynamics of Chagas' disease

A model for the transmission dynamics of Chagas' disease is presented. The structure of the model is similar to that of the Ross-Macdonald model for malaria but includes an extra infectious compartment (chronically ill individuals) which is characteristic of Chagas' disease. In Chagas' disease there are two-main forms of transmission, by blood transfusion and by vector biting. The former is more common in urban environments and the latter is characteristic of rural settings. The characteristic long chronic (frequently asymptomatic) stage of Chagas' disease is potentially a risk factor that could enhance disease transmission by blood transfusion. The model evaluates the relative importance of both transmission modes in populations of constant size. The main results indicate that there is a strong tendency of the disease to reach an asymptotically stable endemic equilibrium point. Also, the magnitude of the basic reproductive number is very sensitive to the length of the chronic stage of the disease and hence it follows that early detection of cases (reducing the length of this stage) is important for the eventual eradication of the disease.