Bob Kooi
Vrije Universiteit Amsterdam, Faculty of Earth and Life Science, Faculty Member
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Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease... more
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analysed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.
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Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease... more
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analysed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.
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The motivation for the research reported in this paper comes from modeling the spread of vector-borne virus diseases. To study the role of the host versus vector dynamics and their interaction we use the susceptible-infected-removed (SIR)... more
The motivation for the research reported in this paper comes from modeling the spread of vector-borne virus diseases. To study the role of the host versus vector dynamics and their interaction we use the susceptible-infected-removed (SIR) host model and the susceptible-infected (SI) vector model. When the vector dynamical processes occur at a faster scale than those in the host-epidemics dynamics, we can use a time-scale argument to reduce the dimension of the model. This is often implemented as a quasi steady-state assumption (qssa) where the slow varying variable is set at equilibrium and an ode equation is replaced by an algebraic equation. Singular perturbation theory will appear to be a useful tool to perform this derivation. An asymptotic expansion in the small parameter that represents the ratio of the two time scales for the dynamics of the host and vector is obtained using an invariant manifold equation. In the case of a susceptible-infected-susceptible (SIS) host model this algebraic equation is a hyperbolic relationship modeling a saturated incidence rate. This is similar to the Holling type II functional response (Ecology) and the Michaelis-Menten kinetics (Biochemistry). We calculate the value for the force of infection leading to an endemic situation by performing a bifurcation analysis. The effect of seasonality is studied where the force of infection changes sinusoidally to model the annual fluctuations of the vector population. The resulting non-autonomous system is studied in the same way as the autonomous system using bifurcation analysis.
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The discreteness–continuity dichotomy in Individual-Based Population Dynamics using massively parrallel machines. 4. Abstract Biological populations consist of discrete individuals with a unique physiological state, which interact among... more
The discreteness–continuity dichotomy in Individual-Based Population Dynamics using massively parrallel machines. 4. Abstract Biological populations consist of discrete individuals with a unique physiological state, which interact among each other on a very local scale. In addition, random variation in, for example, individual growth occurs between fully indentical individuals. In models of population dynamics, this inherent discreteness and the consequent sources of stochasticity are often neglected, because the long–term behavior of populations are more suitably studied with continuous descriptions. A second school of research puts more emphasis on the influence of the inherent stochasticity and less on the full characterisation of the population dynamics as a function of parameters. We propose to study this discreteness–continuity dichotomy using massively parallel machines, since both approaches involve large–scale computation. To resolve the dichotomy comparisons are required b...
Theinventionofthebowandarrowprobablyranksforsocialimpactwiththeinvention of the art of kindling a flre and the invention of the wheel. It must have been in prehistoric times that the flrst missile was launched with a bow, we do not know... more
Theinventionofthebowandarrowprobablyranksforsocialimpactwiththeinvention of the art of kindling a flre and the invention of the wheel. It must have been in prehistoric times that the flrst missile was launched with a bow, we do not know where and when. The event may well have occurred in difierent parts of the world at aboutthe sametime orat widelydifiering times. Numerous kinds of bows are known, they may have long limbs or short limbs, upperandlowerlimbsmaybeequalorunequalinlengthwhilstcross-sectionsofthe limbs may take various shapes. Wood or steel may be used,singly as in ‘self’ bows, or mixed when difierent layers are glued together. There are ‘composite’ bows with layers of several kinds of organic material, wood, sinew and horn, and, in modern forms,layersofwoodandsyntheticplasticsreinforcedwithglassflbreorcarbon. The shapeofthebowwhenrelaxed,maybestraight orrecurved,wherethecurvatureof the partsof the limbsof the unstrungbowis opposite to the way they are ∞exedto fltthe stri...
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Multiple attractors and boundary crises in a tri-trophic food chain
Abstract The need to follow structured populations, as opposed to unstructured ones, is well-recognized. The most detailed category of population models are the individual-based population models (IBMs), also called agent-based population... more
Abstract The need to follow structured populations, as opposed to unstructured ones, is well-recognized. The most detailed category of population models are the individual-based population models (IBMs), also called agent-based population models (ABMs). Their analysis is generally by simulation in time followed by statistical analysis of the numerical results. A less detailed method is the physiologically structured population model approach (PSPMs) leading originally to continuous-time partial differential equations ( pde s) for the p(opulation)-states such as number(-density) with respect to time and i(ndividual)-state such as age and/or size and later to a delay equation formulation. Their mathematical analysis and computational methods are generally complex. Discrete-time matrix population models (MPMs) are much simpler to analyse in all respects, but the applicability is limited due to stringent modelling assumptions made. We discuss here a class of models we call the Cohort Projection Models (CPMs), which were formerly introduced as a special case of PSPMs with pulsed reproduction. CPMs follow cohorts of identical individuals in a Lagrangian way of which the changes of their i-states such as, size, energy reserves and maturity, are described by age dependent ordinary differential equations ( ode )s from DEB theory. Simultaneously the p-states, such as number of individuals are described by time dependent ode s obeying conservation laws. The population is subdivided in generations on the assumption that seasonal cycles synchronize reproduction events among cohorts and all eggs that are produced by different generations are the same. Feedback from the environment can be included via specification of food dynamics that accommodates competition. Temperature follows a specified periodic trajectory in time. This allows for the definition of a projection map of i-states and p-states, from one reproduction event to the next. The projection interval is typically one year for seasonal variability. The properties of the map can be studied using nonlinear dynamical system theory, such as existence and stability of fixed points and, thereby, the long-term dynamics of the food-population system. We demonstrate this using deb parameter values from the Add-my-Pet (AmP) collection for over 2000 animal species, which were estimated from empirical data. CPMs are meant to match the relative simplicity of the analysis of MPMs with the realism of the deb models for the dynamics of the population individuals.
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One way of studying ancient bows is to make replicas and use them for experiments. In the present paper the emphasis is on a different approach, the use of mathematical models. Such models permit theoretical experiments on computers to... more
One way of studying ancient bows is to make replicas and use them for experiments. In the present paper the emphasis is on a different approach, the use of mathematical models. Such models permit theoretical experiments on computers to gain insight into the performance of different types of bow. The use of physical laws and measured quantities, such as the specific mass of materials, in constitutive relations yields mathematical equations. In many cases the complexity of the models obtained will not permit the derivation of the solutions by paper and pencil operations. Computers can then be used to approximate the solution. However, even this procedure will mostly necessitate simplifications. Sometimes essential detailed information is missing. In other situations assumptions need to be made to keep the model manageable. In that case the model has to be validated by the comparison of predicted results with actually measured quantities to justify the assumptions. For that purpose, fo...
A bow is a mechanical device where energy is stored in parts of the limbs that is transferred as kinetic energy to the arrow supported at the middle of the string attached to both limb ends. The energy storage capacity of the material of... more
A bow is a mechanical device where energy is stored in parts of the limbs that is transferred as kinetic energy to the arrow supported at the middle of the string attached to both limb ends. The energy storage capacity of the material of the limbs is crucial to get a high efficiency of this energy transmission. Also the strength of the string is important to make it as light as possible, as well as the quality and reliability the arrow. In this chapter an overview of the materials used in archery equipment is given. Also quality performance criteria for use in shooting at archery tournaments such as Olympic Games, are reviewed and obtained by mathematical modeling of the mechanical function of the bow and arrow. These quality coefficients for the modern bow are only slightly better than those of the historical bows. Materials used in modern working-recurve bows can store more deformation energy per unit of mass than materials used in the past. Moreover the mechanical properties of t...
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The outer sections of the limbs of the composite ‘Asiatic’ bows are stiff and bend backward. In figures and drawings shown in the literature with bows having these rigid ears, however, the angle between the free part of the string and the... more
The outer sections of the limbs of the composite ‘Asiatic’ bows are stiff and bend backward. In figures and drawings shown in the literature with bows having these rigid ears, however, the angle between the free part of the string and the levers is small in braced condition. As an example I mention a drawing of the ‘Omnogov’ bow with sections in Atex and Menes page , and the North Indian and Indo-Persian bows depicted in Latham and Paterson page xxvi and . With some bows the string leaves even the tip of the limbs so that the string is free from the limb except at their nocks, see Boie and Bader Fig. 2:‘Inner Asian . In the present paper I will investigate the influence of the shape of the ears and the reflex at the grip on the performance of the bow. An important question to consider is: why are the ears shaped so that the string leaves the nocks immediately or almost immediately when the bow is drawn? One would expect that the string must have contact with string bridges and leave...
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Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate... more
Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these proces...
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Research Interests: Algorithms, Ecology, Population Dynamics, Biological Sciences, Mathematical Sciences, and 14 morePower Analysis, Standardisation, Bifurcation, Global Attractor, Mathematical Model, Bistability, Three Dimensional, Stoichiometry, Food Chain, Bifurcation Analysis, Asymptotic Behaviour, Mathematical Biosciences, Ordinary Differential Equation, and Limit Cycle
Different extensions of the classical single-strain SIR model for the host population, motivated by modeling dengue fever epidemiology, have reported a rich dynamic structure including deterministic chaos which was able to explain the... more
Different extensions of the classical single-strain SIR model for the host population, motivated by modeling dengue fever epidemiology, have reported a rich dynamic structure including deterministic chaos which was able to explain the large fluctuations of disease incidences. A comparison between the basic two-strain dengue model, which already captures differences between primary and secondary infections, with the four-strain dengue model, that introduces the idea of competition of multiple strains in dengue epidemics shows that the difference between first and secondary infections drives the rich dynamics more than the detailed number of strains to be considered in the model structure. Chaotic dynamics were found to happen at the same parameter region of interest, for both the two and the four-strain models, able to explain the fluctuations observed in empirical data and showing a qualitatively good agreement between empirical data and model simulation. Since the law of parsimony favors the simplest of two competing models, the two-strain model would be the better candidate to be analyzed, giving the expected complex behavior to explain the fluctuations observed in empirical data, and indeed the better option for estimating all initial conditions as well as the few model parameters based on the available incidence data.
Research Interests: Plant Biology and Ecology
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Generally a predator-prey system is modelled by two ordinary differential equations which describe the rate of changes of the biomasses. Since such a system is two-dimensional no chaotic behaviour can occur. In the popular... more
Generally a predator-prey system is modelled by two ordinary differential equations which describe the rate of changes of the biomasses. Since such a system is two-dimensional no chaotic behaviour can occur. In the popular Rosenzweig-MacArthur model, which replaced the Lotka-Volterra model, a stable equilibrium or a stable limit cycle exist. In this paper the prey consumes a non-viable nutrient whose. dynamics is modelled explicitly and this gives an extra ordinary differential equation. For a predator-prey system under chemostat conditions where all parameter values are biologically meaningful, coexistence of multiple chaotic attractors is possible in a narrow region of the two-parameter bifurcation diagram with respect to the chemostat control parameters. Crisis-limited chaotic behaviour and a bifurcation point where two coexisting chaotic attractors merge will be discussed. The interior and boundary crises of this continuous-time predator-prey system look similar to those found f...
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We analyse an epidemiological model of competing strains of pathogens and hence differ- ences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described... more
We analyse an epidemiological model of competing strains of pathogens and hence differ- ences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bi- furcations up to deterministic chaos. Including
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Research Interests: Modeling, Multidisciplinary, Ecological Modelling, Ecosystem Modelling, Weak interaction, and 14 moreFood web, Predation, Nutrient Enrichment, Theoretical Analysis, Nutrient, Intraguild Predation, Spectrum, Ecosystem, Trophic Interaction, Guild, Food Chain, Bifurcation Analysis, Interaction Strength, and Omnivore
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Page 1. ¡¿стог, к-осм gg ^*; дс\ъ 135 8. MODELLING DIRECT (PHOTODEGRADATION) AND INDIRECT (LITTER QUALITY) EFFECTS OF ENHANCED UV-B ON LITTER DECOMPOSITIONJelte Rozema, Bob Kooi*, Rob Broekman and Lothar Kuijper* Department of Systems ...