Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic... 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.
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic... 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.
The motivation for the research reported in this paper comes from modeling the spread of vector-b... 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.
The discreteness–continuity dichotomy in Individual-Based Population Dynamics using massively par... 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... 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...
Abstract The need to follow structured populations, as opposed to unstructured ones, is well-reco... 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.
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic... 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.
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic... 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.
The motivation for the research reported in this paper comes from modeling the spread of vector-b... 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.
The discreteness–continuity dichotomy in Individual-Based Population Dynamics using massively par... 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... 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...
Abstract The need to follow structured populations, as opposed to unstructured ones, is well-reco... 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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