Projects / Programmes
Mathematical studies of infectious disease dynamics
| Code |
Science |
Field |
Subfield |
| 7.00.00 |
Interdisciplinary research |
|
|
| Code |
Science |
Field |
| B110 |
Biomedical sciences |
Bioinformatics, medical informatics, biomathematics biometrics |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
mathematical models, population dynamics, evolution, infectious diseases, dynamical systems, virulence, within-host dynamics, nested models, HIV
Researchers (1)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
29452 |
PhD Barbara Boldin |
Interdisciplinary research |
Head |
2010 - 2012 |
80 |
Organisations (1)
Abstract
The aim of the postdoctoral project is twofold. Firstly, we aim to formulate and analyze several mathematical models in order to answer two specific questions concerning infectious disease dynamics. Secondly, we aim to extend the existing theoretical framework of Adaptive Dynamics and apply the new framework to gain new insights into the evolutionary dynamics of infectious diseases. During the postdoctoral project we aim to deal with the following problems:
(A) Understanding the HIV co-receptor switch:
The first task concerns the within host dynamics of HIV, namely a switch in the co-receptor preference that is observed in about 50% of HIV infected individuals. In the initial stages of an infection, HIV predominantly infects CD4+ T cells that express the CCR5 chemokine receptor. In some individuals, strains emerge later in the infection that use the CXCR4 chemokine receptor in order to gain entry to the cell. This co-receptor switch has important clinical implications because it is associated with a drop in uninfected T cell density and a progression to AIDS.
Up to date, several hypotheses have been proposed to explain the mechanisms underlying the switch in the HIV co-receptor usage, but thus far none of them satisfactorily explained all the features of the switch. We propose that the HIV co-receptor switch can be explained as a consequence of within-host viral evolution in a heterogeneous cell environment and aim to investigate our hypothesis using mathematical models.
(B) The role of immune diversity in the spread and evolution of infectious diseases:
The second task concerns epidemiological and evolutionary dynamics of infectious diseases in heterogeneous populations. Hosts differ in many ways that are relevant for the spread of an infectious disease (e.g., age, social status etc.). We aim to focus in particular on the role of heterogeneity in hosts’ immune responses. Our aim is to develop mathematical models that will allow us to gain understanding of how such differences shape the course of epidemics. We shall also develop models of co-evolutionary dynamics of host populations and pathogens. Such models will allow us to explain (i) how heterogeneity in host populations influences the evolution of an infectious disease and (ii) how, in turn, the pathogens shape the evolution of the diversity in immune responses. We intend to develop a rather general framework and then apply it to specific examples of infectious diseases (influenza, HIV, hepatitis).
(C) Adaptive dynamics with a non-smooth invasion fitness and its applications:
The last part of the project will be devoted to the development of a framework for studying the adaptive evolutionary dynamics for situations where the invasion fitness of a mutant phenotype is not smooth. We will thus extend the existing framework of Adaptive Dynamics that was developed in the 1990s. Our motivation and the need for such an extension comes from the study of nested models of infectious disease dynamics, but the framework can also be applied in other settings, such as in models of adaptive dynamics in allele spaces or in ecological metapopulation models. Furthermore, we aim to apply the newly developed framework to study the mechanisms that lead to so called arms races in pathogen virulence.
Significance for science
The research project had two basic aims:
1. to contribute to our understanding of complex biological phenomena by formulating and analyzing mathematical models
2. to develop new mathematical tools and methods for the analysis of various models in ecology, epidemiology and evolution.
The first goal was achieved with the analysis of two problems. By studying the within-host dynamics of HIV we showed that the co-receptor switch in HIV patients (and all of its important clinical implications) can be understood as a consequence of the adaptation of the virus to the heterogeneous environment within an infected host [1]. We furthermore investigated the eco-evolutionary dynamics of pathogens that are transmitted both directly from one host to another as well as indirectly via an outside environment (contaminated water, soil, household surfaces etc.). Our analysis revealed that the underlying ecological dynamics of the host has important consequences for the evolution of pathogen virulence as well for the evolution of specialism/generalism. Both studies thus shed new light on important biological and medical problems and provide good foundations for further empirical work.
Our second goal was achieved by studying two problems. The first concerns an extension of the theory of Adaptive Dynamics. Adaptive Dynamics was developed in the 1990s to study phenotypic evolution. While the classical Adaptive Dynamics theory represents an important contribution to evolutionary biology (this fact is supported by an increasing number of applications in ecology and epidemiology), some recent examples [2] showed a need for an extension of the existing framework. In [3], we extended the Adaptive Dynamics framework and applied our results to nested models for studying evolution of viruses. New methods were developed also in [5], where we presented new techniques for investigating the role of environmental feedback variables in eco-evolutionary models.
References:
[1] A. Alizon, B. Boldin: Within-host viral evolution in a heterogeneous environment: insights into the HIV co-receptor switch. Journal of Evolutionary Biology, Vol. 23 (2010), pp. 2625-2635
[2] B. Boldin, O. Diekmann: Superinfections can induce evolutionarily stable coexistence of pathogens. Journal of Mathematical Biology, Volume 56 (2008), Issue 5, pp. 635-672.
[3] B. Boldin, O. Diekmann: An extension of the classification of evolutionarily singular strategies in Adaptive Dynamics. Submitted to the Journal of Mathematical Biology
[4] B. Boldin, É. Kisdi: On the evolutionary dynamics of pathogens with direct and environmental transmission. Evolution, Vol. 66, No. 8, (2012), pp. 2514-2527.
[5] Kisdi, É. & Boldin B: A construction method to study the role of incidence in the adaptive dynamics of pathogens with direct and environmental transmission. Journal of Mathematical Biology, Volume 66 (2013), Issue 4-5, pp. 1021–1044
Significance for the country
Mathematics and biology have long been intertwined disciplines: mathematical models are important tools for understanding complex biological phenomena and, in turn, problems in biology and medicine can motivate research in mathematics and often lead to interesting results.
In Slovenia, mathematical biology is still in its infancy: researches in the field of mathematical biology are scarce and mathematical modeling in biology is rarely found among university courses. Interdisciplinary projects like this are thus all the more important for the development of mathematical biology in Slovenia. During the course of the research project we built scientific collaboration between the University of Primorska and some universities that rank among the best in the world in the field of mathematical biology (among others, University of Utrecht and University of Helsinki). In addition, we presented our research results in various scientific events in Slovenia. Such presentations introduce the use of mathematics in biology and medicine to experts in different fields of life sciences and hopefully encourage collaboration between mathematicians and researchers in the field of biology and medicine.
Most important scientific results
Annual report
2010,
2011,
final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Annual report
2010,
2011,
final report,
complete report on dLib.si
