In this paper, we formulate a mathematical model for malaria
transmission that includes incubation periods for both infected human hosts
and mosquitoes. We assume humans gain partial immunity after infection and
divide the infected human population into subgroups based on their infection
history. We derive an explicit formula for the reproductive number of infec-
tion, R0, to determine threshold conditions whether the disease spreads or dies
out. We show that there exists an endemic equilibrium if R0 > 1. Using an
numerical example, we demonstrate that models having the same reproduc-
tive number but different numbers of progression stages can exhibit different
transient transmission dynamics.

We establish the final size equation for a general age-of-infection
epidemic model in a new simpler form if there are no disease deaths (total
population size remains constant). If there are disease deaths, the final size
relation is an inequality but we obtain an estimate for the final epidemic size

Suspended organic and inorganic particles, resulting from the interactions
among biological, physical, and chemical variables, modify the optical
properties of water bodies and condition the trophic chain. The analysis of
their optic properties through the spectral signatures obtained from satellite
images allows us to infer the trophic state of the shallow lakes and generate
a real time tool for studying the dynamics of shallow lakes. Field data
(chlorophyll-a, total solids, and Secchi disk depth) allow us to define levels of
turbidity and to characterize the shallow lakes under study. Using bands 2
and 4 of LandSat 5 TM and LandSat 7 ETM+ images and constructing adequate
artificial neural network models (ANN), a classification of shallow lakes
according to their turbidity is obtained. ANN models are also used to determine
chlorophyll-a and total suspended solids concentrations from satellite
image data. The results are statistically significant. The integration of field
and remote sensors data makes it possible to retrieve information on shallow
lake systems at broad spatial and temporal scales. This is necessary to understanding
the mechanisms that affect the trophic structure of these ecosystems.

Temperate-zone bats are subject to serious energetic constraints
due to their high surface area to volume relations, the cost of temperature reg-
ulation, the high metabolic cost of flight, and the seasonality of their resources.
We present a novel, multilevel theoretical approach that integrates information
on bat biology collected at a lower level of organization, the individual with its
physiological characteristics, into a modeling framework at a higher level, the
population. Our individual component describes the growth of an individual
female bat by modeling the dynamics of the main body compartments (lipids,
proteins, and carbohydrates). A structured population model based on ex-
tended McKendrick-von Foerster partial differential equations integrates those
individual dynamics and provides insight into possible regulatory mechanisms
of population size as well as conditions of population survival and extinction.
Though parameterized for a specific bat species, all modeling components can
be modified to investigate other bats with similar life histories. A better un-
derstanding of population dynamics in bats can assist in the development of
management techniques and conservation strategies, and to investigate stress
effects. Studying population dynamics of bats presents particular challenges,
but bats are essential in some areas of concern in conservation and disease
ecology that demand immediate investigation.

A multiple species metapopulations model with density-dependent
dispersal is presented. Assuming the network configuration matrix to be di-
agonizable we obtain a decoupling of the associated perturbed system from
the homogeneous state. It was possible to analyze in detail the instability in-
duced by the density-dependent dispersal in two classes of k-species interaction
models: a hierarchically organized competitive system and an age-structured
model.

A spatially explicit model is developed to simulate the small fish
community and its underlying food web, in the freshwater marshes of the Everglades.
The community is simplified to a few small fish species feeding on
periphyton and invertebrates. Other compartments are detritus, crayfish, and
a piscivorous fish species. This unit food web model is applied to each of the
10,000 spatial cells on a 100 x 100 pixel landscape. Seasonal variation in water
level is assumed and rules are assigned for fish movement in response to
rising and falling water levels, which can cause many spatial cells to alternate
between flooded and dry conditions. It is shown that temporal variations of
water level on a spatially heterogeneous landscape can maintain at least three
competing fish species. In addition, these environmental factors can strongly
affect the temporal variation of the food web caused by top-down control from
the piscivorous fish.

Most animal populations are characterized by balanced sex ratios,
but there exist several exceptions in which the sex ratio at birth is skewed. An
interesting hypothesis proposed by Clark (1978) to explain male-biased sex ratios
is the local resource competition theory: the bias may be expected in those
species in which males disperse more than females, which are thus more prone
to local competition for resources. Here we discuss some of the ideas underlying
Clark’s theory using a spatially explicit approach. In particular, we focus
on the role of spatiotemporal heterogeneity as a possible determinant of biased
sex ratios. We model spatially structured semelparous populations where
either Ricker density dependence or environmental stochasticity can generate
irregular spatiotemporal patterns. The proposed discrete-time model describes
both genetic and complex population dynamics assuming that (1) sex ratio is
genetically determined, (2) only young males can disperse, and (3) individuals
locally compete for resources. The analysis of the model shows that no skewed
sex ratios can arise in homogeneous habitats. Temporal asynchronized fluctuations
between two distinct patches coupled with dispersal of young males is the
minimum requirement for obtaining skewed sex ratios of demographic nature
in local adult populations. However, the establishment of a male-biased sex
ratio at birth in the long run is possible if dispersal is genetically determined
and there is genetic linkage between sex ratio determination and dispersal.

The dynamic behaviour of simple aquatic ecosystems with nutrient
recycling in a chemostat, stressed by limited food availability and a toxicant, is
analysed. The aim is to find effects of toxicants on the structure and functioning
of the ecosystem. The starting point is an unstressed ecosystem model for
nutrients, populations, detritus and their intra- and interspecific interactions,
as well as the interaction with the physical environment. The fate of the toxicant
includes transport and exchange between the water and the populations
via two routes, directly from water via diffusion over the outer membrane of
the organism and via consumption of contaminated food. These processes are
modelled using mass-balance formulations and diffusion equations. At the population
level the toxicant affects different biotic processes such as assimilation,
growth, maintenance, reproduction, and survival, thereby changing their biological
functioning. This is modelled by taking the parameters that described
these processes to be dependent on the internal toxicant concentration. As a
consequence, the structure of the ecosystem, that is its species composition,
persistence, extinction or invasion of species and dynamics behaviour, steady
state oscillatory and chaotic, can change. To analyse the long-term dynamics
we use the bifurcation analysis approach. In ecotoxicological studies the
concentration of the toxicant in the environment can be taken as the bifurcation
parameter. The value of the concentration at a bifurcation point marks
a structural change of the ecosystem. This indicates that chemical stressors
are analysed mathematically in the same way as environmental (e.g. temperature)
and ecological (e.g. predation) stressors. Hence, this allows an integrated
approach where different type of stressors are analysed simultaneously. Environmental
regimes and toxic stress levels at which no toxic effects occur and
where the ecosystem is resistant will be derived. A numerical continuation
technique to calculate the boundaries of these regions will be given.

Viral infections are one of the leading source of mortality world-
wide. The great majority of them circulate and persist in wild reservoirs and
periodically spill over into humans or domestic animals. In the wild reservoirs,
the progression of disease is frequently quite different from that in spillover
hosts. We propose a mathematical treatment of the dynamics of viral infec-
tions in wild mammals using models with alternative outcomes. We develop
and analyze compartmental epizootic models assuming permanent or tempo-
rary immunity of the individuals surviving infections and apply them to rabies
in bats. We identify parameter relations that support the existing patterns in
the viral ecology and estimate those parameters that are unattainable through
direct measurement. We also investigate how the duration of the acquired
immunity affects the disease and population dynamics.

Negative frequency-dependent selection is a well known microevo-
lutionary process that has been documented in a population of Perissodus mi-
crolepis, a species of cichlid fish endemic to Lake Tanganyika (Africa). Adult
P. microlepis are lepidophages, feeding on the scales of other living fish. As an
adaptation for this feeding behavior P. microlepis exhibit lateral asymmetry
with respect to jaw morphology: the mouth either opens to the right or left
side of the body. Field data illustrate a temporal phenotypic oscillation in the
mouth-handedness, and this oscillation is maintained by frequency-dependent
selection. Since both genetic and population dynamics occur on the same time
scale in this case, we develop a (discrete time) model for P. microlepis popu-
lations that accounts for both dynamic processes. We establish conditions on
model parameters under which the model predicts extinction and conditions
under which there exists a unique positive (survival) equilibrium. We show
that at the positive equilibrium there is a 1:1 phenotypic ratio. Using a lo-
cal stability and bifurcation analysis, we give further conditions under which
the positive equilibrium is stable and conditions under which it is unstable.
Destabilization results in a bifurcation to a periodic oscillation and occurs
when frequency-dependent selection is sufficiently strong. This bifurcation is
offered as an explanation of the phenotypic frequency oscillations observed in
P. microlepis. An analysis of the bifurcating periodic cycle results in some
interesting and unexpected predictions.

We constructed differential equation models for the diurnal abundance
and distribution of breeding glaucous-winged gulls (Larus glaucescens)
as they moved among nesting and non-nesting habitat patches. We used time
scale techniques to reduce the differential equations to algebraic equations and
connected the models to field data. The models explained the data as a function
of abiotic environmental variables with R2 = 0.57. A primary goal of this
study is to demonstrate the utility of a methodology that can be used by ecologists
and wildlife managers to understand and predict daily activity patterns
in breeding seabirds.

The increasing prevalence of HIV/AIDS in Africa over the past
twenty-five years continues to erode the continent’s health care and overall
welfare. There have been various responses to the pandemic, led by Uganda,
which has had the greatest success in combating the disease. Part of Uganda’s
success has been attributed to a formalized information, education, and com-
munication (IEC) strategy, lowering estimated HIV/AIDS infection rates from
18.5% in 1995 to 4.1% in 2003. We formulate a model to investigate the ef-
fects of information and education campaigns on the HIV epidemic in Uganda.
These campaigns affect people’s behavior and can divide the susceptibles class
into subclasses with different infectivity rates. Our model is a system of or-
dinary differential equations and we use data about the epidemics and the
number of organizations involved in the campaigns to estimate the model pa-
rameters. We compare our model with three types of susceptibles to a standard
SIR model.

Arenaviruses are associated with rodent-transmitted diseases in
humans. Five arenaviruses are known to cause human illness: Lassa virus,
Junin virus, Machupo virus, Guanarito virus and Sabia virus. In this investigation,
we model the spread of Machupo virus in its rodent host Calomys
callosus. Machupo virus infection in humans is known as Bolivian hemorrhagic
fever (BHF) which has a mortality rate of approximately 5-30% [31].
Machupo virus is transmitted among rodents through horizontal (direct
contact), vertical (infected mother to offspring) and sexual transmission. The
immune response differs among rodents infected with Machupo virus. Either
rodents develop immunity and recover (immunocompetent) or they do not develop
immunity and remain infected (immunotolerant). We formulate a general
deterministic model for male and female rodents consisting of eight differential
equations, four for females and four for males. The four states represent susceptible,
immunocompetent, immunotolerant and recovered rodents, denoted
as S, It, Ic and R, respectively. A unique disease-free equilibrium (DFE) is
shown to exist and a basic reproduction number R0 is computed using the next
generation matrix approach. The DFE is shown to be locally asymptotically
stable if R0 1.
Special cases of the general model are studied, where there is only one
immune stage, either It or Ic. In the first model, SIcRc, it is assumed that all
infected rodents are immunocompetent and recover. In the second model, SIt,
it is assumed that all infected rodents are immunotolerant. For each of these
models, the basic reproduction numbers are computed and their relationship
to the basic reproduction number of the general model determined. For the
SIt model, it is shown that bistability may occur, the DFE and an enzootic
equilibrium, with all rodents infectious, are locally asymptotically stable for the
same set of parameter values. A simplification of the SIt model yields a third
model, where the sexes are not differentiated, and therefore, there is no sexual
transmission. For this third simplified model, the dynamics are completely
analyzed. It is shown that there exists a DFE and possibly two additional
equilibria, one of which is globally asymptotically stable for any given set of
parameter values; bistability does not occur. Numerical examples illustrate the
dynamics of the models. The biological implications of the results and future
research goals are discussed in the conclusion.

Species augmentation is a method of reducing species loss via augmenting
declining or threatened populations with individuals from captive-bred
or stable, wild populations. In this paper, we develop a differential equations
model and optimal control formulation for a continuous time augmentation of
a general declining population. We find a characterization for the optimal control
and show numerical results for scenarios of different illustrative parameter
sets. The numerical results provide considerably more detail about the exact
dynamics of optimal augmentation than can be readily intuited. The work and
results presented in this paper are a first step toward building a general theory
of population augmentation, which accounts for the complexities inherent in
many conservation biology applications.

We develop a numerical method for estimating parameters in a
structured erythropoiesis model consisting of a nonlinear system of partial differential
equations. Convergence theory for the computed parameters is provided.
Numerical results for estimating the growth rate of precursor cells as a
function of the erythropoietin concentration and the decay rate of erythropoietin
as a function of the total number of precursor cells from computationally
generated data are provided. Standard errors for such parameters are also
given.

We consider ordinary least squares parameter estimation problems
where the unknown parameters to be estimated are probability distributions.
A computational framework for quantification of uncertainty (e.g., standard
errors) associated with the estimated parameters is given and sample numerical
findings are presented.

In this study, we expand on the susceptible-infected-susceptible
(SIS) heterosexual mixing setting by including the movement of individuals of
both genders in a spatial domain in order to more comprehensively address the
transmission dynamics of competing strains of sexually-transmitted pathogens.
In prior models, these transmission dynamics have only been studied in the
context of nonexplicitly mobile heterosexually active populations at the demo-
graphic steady state, or, explicitly in the simplest context of SIS frameworks
whose limiting systems are order preserving. We introduce reaction-diffusion
equations to study the dynamics of sexually-transmitted diseases (STDs) in
spatially mobile heterosexually active populations. To accomplish this, we
study a single-strain STD model, and discuss in what forms and at what speed
the disease spreads to noninfected regions as it expands its spatial range. The
dynamics of two competing distinct strains of the same pathogen on this pop-
ulation are then considered. The focus is on the investigation of the spatial
transition dynamics between the two endemic equilibria supported by the non-
spatial corresponding model. We establish conditions for the successful inva-
sion of a population living in endemic conditions by introducing a strain with
higher fitness. It is shown that there exists a unique spreading speed (where
the spreading speed is characterized as the slowest speed of a class of traveling
waves connecting two endemic equilibria) at which the infectious population
carrying the invading stronger strain spreads into the space where an equi-
librium distribution has been established by the population with the weaker
strain. Finally, we give sufficient conditions under which an explicit formula
for the spreading speed can be found.

In this paper, the existence of positive periodic solutions of a class
of periodic n-species Gilpin-Ayala impulsive competition systems is studied.
By using the continuation theorem of coincidence degree theory, a set of easily
verifiable sufficient conditions is obtained. Our results are general enough to
include some known results in this area.

Simple, discrete-time, population models typically exhibit complex
dynamics, like cyclic oscillations and chaos, when the net reproductive
rate, R, is large. These traditional models generally do not incorporate variability
in juvenile “risk,” defined to be a measure of a juvenile’s vulnerability to
density-dependent mortality. For a broad class of discrete-time models we show
that variability in risk across juveniles tends to stabilize the equilibrium. We
consider both density-independent and density-dependent risk, and for each,
we identify appropriate shapes of the distribution of risk that will stabilize the
equilibrium for all values of R. In both cases, it is the shape of the distribution
of risk and not the amount of variation in risk that is crucial for stability.