Impact of resource distributions on the competition of species in stream environment.

Our earlier work in Nguyen et al. (Maximizing metapopulation growth rate and biomass in stream networks. arXiv preprint arXiv:2306.

A mathematical model for Vibrio-phage interactions.

A cholera model has been formulated to incorporate the interaction of bacteria and phage. It is shown that there may exist three equilibria: one disease free and two endemic equilibria. Threshold parameters have been derived to characterize stability of these equilibria.

Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix.

The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number [Formula: see text] is strictly decreasing with respect to the dispersal rate of the infected individuals. When [Formula: see text], the model admits a unique endemic equilibrium, and its asymptotic profiles are characterized for small dispersal rates.

A general theory for target reproduction numbers with applications to ecology and epidemiology.

A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identifies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied to the analysis of single and multiple control strategies in ecology and epidemiology, and this provides new biological insights.

A mathematical model of syphilis transmission in an MSM population.

Syphilis is caused by the bacterium Treponema pallidum subspecies pallidum, and is a sexually transmitted disease with multiple stages. A model of transmission of syphilis in an MSM population (there has recently been a resurgence of syphilis in such populations) that includes infection stages and treatment is formulated as a system of ordinary differential equations. The control reproduction number is calculated, and it is proved that if this threshold parameter is below one, syphilis dies out; otherwise, if it is greater than one, it is shown that there exists a unique endemic equilibrium and that for certain special cases, this equilibrium is globally asymptotically stable.

Disease invasion risk in a growing population.

The spread of an infectious disease may depend on the population size. For simplicity, classic epidemic models assume homogeneous mixing, usually standard incidence or mass action. For standard incidence, the contact rate between any pair of individuals is inversely proportional to the population size, and so the basic reproduction number (and thus the initial exponential growth rate of the disease) is independent of the population size.

Models of bovine babesiosis including juvenile cattle.

Bovine Babesiosis in cattle is caused by the transmission of protozoa of Babesia spp. by ticks as vectors. Juvenile cattle (<9 months of age) have resistance to Bovine Babesiosis, rarely show symptoms, and acquire immunity upon recovery.

Modelling and control of cholera on networks with a common water source.

A mathematical model is formulated for the transmission and spread of cholera in a heterogeneous host population that consists of several patches of homogeneous host populations sharing a common water source. The basic reproduction number ℛ0 is derived and shown to determine whether or not cholera dies out. Explicit formulas are derived for target/type reproduction numbers that measure the control strategies required to eradicate cholera from all patches.

Disease invasion on community networks with environmental pathogen movement.

The ability of disease to invade a community network that is connected by environmental pathogen movement is examined. Each community is modeled by a susceptible-infectious-recovered (SIR) framework that includes an environmental pathogen reservoir, and the communities are connected by pathogen movement on a strongly connected, weighted, directed graph. Disease invasibility is determined by the basic reproduction number R(0) for the domain.

Dynamics of an age-of-infection cholera model.

A new model for the dynamics of cholera is formulated that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is defined and proved to be a sharp threshold determining whether or not cholera dies out. Final size relations for cholera outbreaks are derived for simplified models when input and death are neglected.

A cholera model in a patchy environment with water and human movement.

A mathematical model for cholera is formulated that incorporates direct and indirect transmission, patch structure, and both water and human movement. The basic reproduction number R0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoff's Matrix Tree Theorem from graph theory is used to investigate the dependence of R0 on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when R0>1.

Extending the type reproduction number to infectious disease control targeting contacts between types.

A new quantity called the target reproduction number is defined to measure control strategies for infectious diseases with multiple host types such as waterborne, vector-borne and zoonotic diseases. The target reproduction number includes as a special case and extends the type reproduction number to allow disease control targeting contacts between types. Relationships among the basic, type and target reproduction numbers are established.

Impact of heterogeneity on the dynamics of an SEIR epidemic model.

An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number R0 gives a sharp threshold.

Reproduction numbers for infections with free-living pathogens growing in the environment.

The basic reproduction number ℛ(0) for a compartmental disease model is often calculated by the next generation matrix (NGM) approach. When the interactions within and between disease compartments are interpreted differently, the NGM approach may lead to different ℛ(0) expressions. This is demonstrated by considering a susceptible-infectious-recovered-susceptible model with free-living pathogen (FLP) growing in the environment.

Cholera models with hyperinfectivity and temporary immunity.

A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number R(0) is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels.

Global dynamics of cholera models with differential infectivity.

A general compartmental model for cholera is formulated that incorporates two pathways of transmission, namely direct and indirect via contaminated water. Non-linear incidence, multiple stages of infection and multiple states of the pathogen are included, thus the model includes and extends cholera models in the literature. The model is analyzed by determining a basic reproduction number R0 and proving, by using Lyapunov functions and a graph-theoretic result based on Kirchhoff's Matrix Tree Theorem, that it determines a sharp threshold.