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1.
We will be concerned with optimal intervention policies for a continuous-time stochastic SIR (susceptible-->infective-->removed) model for the spread of infection through a closed population. In previous work on such optimal policies, it is common to assume that model parameter values are known; in reality, uncertainty over parameter values exists. We shall consider the effect upon the optimal policy of changes in parameter estimates, and of explicitly taking into account parameter uncertainty via a Bayesian decision-theoretic framework. We consider policies allowing for (i) the isolation of any number of infectives, or (ii) the immunisation of all susceptibles (total immunisation). Numerical examples are given to illustrate our results. 相似文献
2.
Interaction of maturation delay and nonlinear birth in population and epidemic models 总被引:16,自引:0,他引:16
A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e−
d
1
T−dN(t) governs the adult population, with the death rate in previous life stages d
1≧0. Standard assumptions are made on B(N) so that a unique equilibrium N
e
exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d
1>0, as T increases the equilibrium N
e
can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease
that does not cause death is introduced into the population, a threshold parameter R
0 is identified. When R
0<1, the disease dies out; when R
0>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations
indicate that oscillations can also be induced by disease related death in a model with maturation delay.
Received: 2 November 1998 / Revised version: 26 February 1999 相似文献
3.
Analysis of an SEIRS epidemic model with two delays 总被引:29,自引:0,他引:29
A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed
susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and
immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional
to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the
disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated.
The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the
SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the
two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero.
Received 8 May 1995; received in revised form 7 November 1995 相似文献
4.
Optimal control of the chemotherapy of HIV 总被引:7,自引:0,他引:7
Using an existing ordinary differential equation model which describes the interaction of the immune system with the human
immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then
solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral
production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing
the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system
composed of four ordinary differential equations and four adjoint ordinary differential equations.
Received 5 July 1995; received in revised form 3 June 1996 相似文献
5.
Two SIS epidemiologic models with delays 总被引:8,自引:0,他引:8
The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the
population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here
the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population
dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics,
periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter
values.
Received: 10 January 1997 / 18 November 1997 相似文献
6.
Horst Behncke 《Journal of mathematical biology》1997,35(4):375-390
In [2] the author has developed an optimization model for the force and energy in competitive running. In this paper the
energy processes in the muscle were described by a three-compartment hydraulic model. Here this is reviewed briefly and applied
to the current world records in order to determine the key parameters, maximal force, energy reserves and oxygen uptake. These
values agree well with those given in the literature and those obtained by other means. The velocity profiles for 100 m sprints
are described equally well. The model is then applied to older world records to deduce a relation between the force and energy
by linear regression. Finally the fully parameterized model is used to compute the effects of adverse wind and altitude. Inasmuch
as there are data available, there is a good agreement.
Received 19 July 1995; received in revised form 27 February 1996 相似文献
7.
Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion
in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with
brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting
dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications
thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave
patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators
providing input to a kinematic musculature model of lamprey..
Received: 25 November 1996 / Revised version: 9 December 1997 相似文献
8.
We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type.
It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive
almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others.
The existence of an almost periodic global attractor is also discussed.
Received: 11 November 1996 / Revised version: 8 January 1998 相似文献
9.
A model for macroparasitic infection with variable aggregation is considered. The starting point is an immigration-and-death
process for parasites within a host, as in [3]; it is assumed however that infections will normally occur with several larvae
at the same time. Starting from here, a four-dimensional, where free-living larvae are explicitly considered, and a three-dimensional
model are obtained with same methods used in [26]. The equilibria of these models are found, their stability is discussed,
as well as some qualitative features. It has been found that the assumption of “clumped” infections may have dramatic effects
on the aggregation exhibited by these models. Infections with several larvae at the same time also increases the stability
of the endemic equilibria of these models, and makes the occurrence of subcritical bifurcations (and consequently multiple
equilibria) slightly more likely.
The results of the low-dimensional model have also been compared to numerical simulations of the infinite system that describes
the immigration-and-death process. It appears that the results of the systems are, by and large, in close correspondence,
except for a parameter region where the four-dimensional model exhibits unusual properties, such as the occurrence of multiple
disease-free equilibria, that do not appear to be shared by the infinite system.
Received 28 October 1996; in revised form 11 April 1997 相似文献
10.
Odo Diekmann Mats Gyllenberg J. A. J. Metz Horst R. Thieme 《Journal of mathematical biology》1998,36(4):349-388
—We define a linear physiologically structured population model by two rules, one for reproduction and one for “movement”
and survival. We use these ingredients to give a constructive definition of next-population-state operators. For the autonomous
case we define the basic reproduction ratio R
0 and the Malthusian parameter r and we compute the resolvent in terms of the Laplace transform of the ingredients. A key feature of our approach is that
unbounded operators are avoided throughout. This will facilitate the treatment of nonlinear models as a next step.
Received 26 July 1996; received in revised form 3 September 1997 相似文献
11.
We contribute to the discussion of causes and effects of aggregation (overdispersion) of macroparasite counts, focussing
particularly upon the effects of clumped infections and parasite-induced host mortality. The simple nonlinear stochastic model
for the evolution of the parasite load of a single host, investigated in Isham (1995), is extended to allow three parasite
stages (larval, mature and offspring), and to allow durations of these stages to be non-exponentially distributed. As in the
earlier work, exact algebraic results are possible, providing insight into the aggregation mechanisms, as long as the only
source of interaction between host and parasites is an excess host mortality linearly related to the parasite load. Results
are obtained on the distribution of parasite lad and on host survival. In particular, although parasite-induced host mortality
is usually thought of as a process that reduces parasite aggregation (Anderson and Gordon 1982), it is shown that, for this
model, parasite-induced host mortality cannot cause the index of dispersion to fall below unity. Host heterogeneity and disease
control are also discussed. An approximation based on moment assumptions appropriate to a specially-constructed multivariate
negative binomial distribution is proposed. This approximation, which is applicable to other processes, and an alternative
based on the multivariate normal distribution are compared with exact results.
Received: 17 December 1998 / Revised version: 2 June 1999 相似文献
12.
Hugo A. van den Berg Yuri N. Kiselev S. A. L. M. Kooijman Michael V. Orlov 《Journal of mathematical biology》1998,37(1):28-48
A microbial trichome grows by assimilating nutrients from its environment, and converting these into catalytic macro-molecular
machinery. This machinery may be divided into assimilatory machinery and proliferative machinery. The former type is involved
in nutrient uptake, whereas the latter type enables the trichome to grow. The cells in the trichome are faced with an allocation
problem: given the availability of nutrients in the environment, how many macro-molecular building blocks should be allocated
to the synthesis of assimilatory machinery, and how many to the synthesis of proliferative machinery? We answer this question
for a particular model, which is a generalization of the Droop quota model. We formulate a two-dimensional non-linear optimal
control problem, corresponding to this model. An optimal allocation regime with a singular segment is derived, based on Pontryagin’s
maximum principle. We give a direct proof of optimality. We discuss how actual biological cells might implement this optimal
regime.
Received: 16 December 1996 / Revised version: 14 September 1997 相似文献
13.
The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells
can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and
growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod
model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations
is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis
growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive
mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing
modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding
to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative
feature of some experimental data which show that the population density of the winning species approaches a positive steady
state via transient oscillations while that of the losing species approaches the zero steady state monotonically.
Received 4 August 1995; received in revised form 15 December 1995 相似文献
14.
Optimal harvesting of stochastically fluctuating populations 总被引:5,自引:0,他引:5
We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under
the most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model
where there are constraints on the admissible harvesting rates. We use stochastic calculus to derive the optimal population
threshold at which individuals are harvested as well as the overall value of the population in the sense of the model. We
show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution which we find explicitly. Needless to say, our results
prove that any strategy which totally depletes the population is sub-optimal. These results are much more precise than those
previously obtained for this problem.
Received 24 June 1996; received in revised form 7 April 1997 相似文献
15.
. We introduce some special chiasma formation processes. First a family of discrete chiasma formation processes is introduced
and we determine the nature of higher order interference associated with those processes. Secondly we consider a two-stage
chiasma formation process, where the associated recombination frequency between two markers depends not only on their map
distance but also on their location along the chromosomes. We characterise under this process, in some cases, the nature of
interference between two segments.
Received: 22 January 1996 / Revised version: 17 September 1997 相似文献
16.
We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent
and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem
being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system
to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic,
just as suggested by the instability of the endemic steady state.
Received: 1 September 1995 / Revised version: 30 April 1997 相似文献
17.
Della Corte L Crichton RR Duburs G Nolan K Tipton KF Tirzitis G Ward RJ 《Amino acids》2002,23(4):367-379
Summary. Despite the multitude of evidence for the beneficial effects of taurine supplementation in a variety of disease, the underlying
modifying action of taurine with respect to either molecular or biochemical mechanisms is almost totally unknown. We have
assessed the development of taurine analogues, particularly where there has been substitution at the suphonate or amine group.
Such substitutions allow the investigator to probe the relationship between structure and function of the taurine molecule.
In addition such studies should help to ascertain taurine's point of interaction with the effector molecule. These results
will prepare the way for the development of the second generation of taurine analogues.
Received January 2, 2002 Accepted January 28, 2002 Published online August 30, 2002
Acknowledgements This research has been funded by the COST Chemistry programmes COST D8 “Chemistry of Metals in Medicine” and D-13 “New Molecules
for Human Health Care”. All of the authors are members of the Working Group D13/0011/00 “Investigation of mechanisms underlying
the pharmacological actions of taurine upon cell apoptosis and calcium homeostasis”.
Authors' address: Dr. R.J. Ward, Unite de Biochimie, Catholic Universite de Louvain, Place Louis Pasteur 1, B-1348 Louvain-la-Neuve, Belgium,
E-mail: ward@bioc.ucl.ac.be 相似文献
18.
In this paper we propose a general framework for discrete time one-dimensional Markov population models which is based on
two fundamental premises in population dynamics. We show that this framework incorporates both earlier population models,
like the Ricker and Hassell models, and experimental observations concerning the structure of density dependence. The two
fundamental premises of population dynamics are sufficient to guarantee that the model will exhibit chaotic behaviour for
high values of the natural growth and the density-dependent feedback, and this observation is independent of the particular
structure of the model. We also study these models when the environment of the population varies stochastically and address
the question under what conditions we can find an invariant probability distribution for the population under consideration.
The sufficient conditions for this stochastic stability that we derive are of some interest, since studying certain statistical
characteristics of these stochastic population processes may only be possible if the process converges to such an invariant
distribution.
Received 15 May 1995; received in revised form 17 April 1996 相似文献
19.
We examine some simple population models that incorporate a time delay which is not a constant but is instead a known periodic function of time. We examine what effect this periodic variation has on the linear stability of the equilibrium states of scalar population models and of a simple predator prey system. The case when the delay differs from a constant by a small amplitude periodic perturbation can be treated analytically by using two-timing methods. Of particular interest is the case when the system is initially marginally stable. The introduction of variation in the delay can then have either a stabilising effect or a destabilizing one, depending on the frequency of the periodic perturbation. The case when the periodic perturbation has large amplitude is studied numerically. If the fluctuation is large enough the effect can be stabilising. 相似文献
20.
The effect of overcompensatory recruitment and the combined effect of overcompensatory recruitment and generation delay in
discrete nonlinear age-structured population models is studied. Considering overcompensatory recruitment alone, we present
formal proofs of the supercritical nature of bifurcations (both flip and Hopf) as well as an extensive analysis of dynamics
in unstable parameter regions. One important finding here is that in case of small and moderate year to year survival probabilities
there are large regions in parameter space where the qualitative behaviour found in a general n+1 dimensional model is retained already in a one-dimensional model. Another result is that the dynamics at or near the boundary
of parameter space may be very complicated. Generally, generation delay is found to act as a destabilizing effect but its
effect on dynamics is by no means unique. The most profound effect occurs in the n-generation delay cases. In these cases there is no stable equilibrium X
* at all, but whenever X
* small, a stable cycle of period n+1 where the periodic points in the cycle are on a very special form. In other cases generation delay does not alter the dynamics
in any substantial way.
Received 25 April 1995; received in revised form 21 November 1995 相似文献