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.

Transmission dynamics of two dengue serotypes with vaccination scenarios.

In this work we present a mathematical model that incorporates two Dengue serotypes. The model has been constructed to study both the epidemiological trends of the disease and conditions that allow coexistence in competing strains under vaccination. We consider two viral strains and temporary cross-immunity with one vector mosquito population. Results suggest that vaccination scenarios will not only reduce disease incidence but will also modify the transmission dynamics. Indeed, vaccination and cross immunity period are seen to decrease the frequency and magnitude of outbreaks but in a differentiated manner with specific effects depending upon the interaction vaccine and strain type.

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.

Detachment and diffusive-convective transport in an evolving heterogeneous two-dimensional biofilm hybrid model.

Under the hypothesis of correlation between biofilm survival and nutrient availability, by considering fluid drag forces and mortality due to nutrient depletion, a biofilm detachment/breaking condition is derived. The mechanisms leading to biofilm detachment/breaking are discussed. We construct and describe a hybrid model for a heterogeneous biofilm attached to walls in a channel where liquid is flowing. The model is called hybrid because it couples conservation equations with a cellular automaton. The biofilm layer is viewed as a porous medium with variable porosity, tortuosity, and permeability. The model is solved using asymptotic and finite differences methods. Results for porosity, nutrient distribution, and average surface location are presented. The model is capable of reproducing biofilm heterogeneity as well as the typical surface fingering (mushroomlike structure).

Could widespread use of combination antiretroviral therapy eradicate HIV epidemics?

Current combination antiretroviral therapies (ARV) are widely used to treat HIV. However drug-resistant strains of HIV have quickly evolved, and the level of risky behaviour has increased in certain communities. Hence, currently the overall impact that ARV will have on HIV epidemics remains unclear. We have used a mathematical model to predict whether the current therapies: are reducing the severity of HIV epidemics, and could even lead to eradication of a high-prevalence (30%) epidemic. We quantified the epidemic-level impact of ARV on reducing epidemic severity by deriving the basic reproduction number (R(0)(ARV)). R(0)(ARV) specifies the average number of new infections that one HIV case generates during his lifetime when ARV is available and ARV-resistant strains can evolve and be transmitted; if R(0)(ARV) is less than one epidemic eradication is possible. We estimated for the HIV epidemic in the San Francisco gay community (using uncertainty analysis), the present day value of R(0)(ARV), and the probability of epidemic eradication. We assumed a high usage of ARV and three behavioural assumptions: that risky sex would (1) decrease, (2) remain stable, or (3) increase. Our estimated values of R(0)(ARV) (median and interquartile range [IQR]) were: 0.90 (0.85-0.96) if risky sex decreases, 1.0 (0.94-1.05) if risky sex remains stable, and 1.16 (1.05-1.28) if risky sex increases. R(0)(ARV) decreased as the fraction of cases receiving treatment increased. The probability of epidemic eradication is high (p=0.85) if risky sex decreases, moderate (p=0.5) if levels of risky sex remain stable, and low (p=0.13) if risky sex increases. We conclude that ARV can function as an effective HIV-prevention tool, even with high levels of drug resistance and risky sex. Furthermore, even a high-prevalence HIV epidemic could be eradicated using current ARV.

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.

Density-dependent dynamics and superinfection in an epidemic model.

A mathematical model of the interaction between two pathogen strains and a single host population is studied. Variable population size, density-dependent mortality, disease-related deaths (virulence), and superinfection are incorporated into the model. Results indicate that coexistence of the two strains is possible depending on the magnitude of superinfection. Global asymptotic stability of the steady-state that gives coexistence for both strains under suitable and biologically feasible constraints is proved.

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.

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.

Community treatment of HIV-1: initial stage and asymptotic dynamics.

Treatment with antiviral drugs (zidovudine and ddI) has been reported to delay progression to AIDS, and may even possibly lower the infectiousness of the infectives. However, its effect on the community level is still uncertain. The latter is important since a successful community treatment program must meet both public health and individual health goals. Our study will focus on the effect of a community-wide treatment program initiated at the early stages of the disease as well as the long-term effect of the program. Using a simple mathematical model, we demonstrate that a community-wide treatment program could be instrumental in decreasing HIV incidence rate and eradicating the disease in the future if certain conditions on the parameters are met. On the other hand, when the above mentioned conditions on the parameters are not satisfied, we show that even if the treatment does improve survival in AIDS patients and decrease the rate at which HIV infection spreads in the community, it is still possible for the treatment program to have an adverse effect on the spread of AIDS in the population in the long run. Hence, a public health policy maker must exercise caution in order to design an effective treatment program for HIV/AIDS.

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.

Habitat suitability and herbivore dynamics.

We derive a dynamic model for a plant herbivore system describing the interaction of a gall-forming aphid and a single plant. We compare the behavior of our model with experimental observations obtained from an aphid plant system studied by Whitham (Whitham, T.G. 1978, Habitat selection of Pemphigus aphids in response to resource limitation and competition. Ecology 59, 1164-1176). A simple parameter estimation shows a close correlation between the predicted and observed results.

Modelling the effect of treatment and behavioral change in HIV transmission dynamics.

In this paper we analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical/therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV. The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection/treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.

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.