Mathematics inspired by immuno-epidemiology

Transcription

1 Mathematics inspired by immuno-epidemiology The American Institute of Mathematics The following compilation of participant contributions is only intended as a lead-in to the AIM workshop Mathematics inspired by immuno-epidemiology. This material is not for public distribution. Corrections and new material are welcomed and can be sent to workshops@aimath.org Version: Wed Aug 19 09:50:

2 2 Table of Contents A. Participant Contributions Agusto, Folashade 2. Baez, Javier 3. Belair, Jacques 4. Childs, Lauren 5. Feng, Zhilan 6. Glasser, John 7. Gulbudak, Hayriye 8. Gumel, Abba 9. Heffernan, Jane 10. Lenhart, Suzanne 11. Li, Jing 12. Magpantay, Felicia Maria 13. Numfor, Eric 14. Pell, Bruce 15. Perelson, Alan 16. Pugliese, Andrea 17. Thieme, Horst 18. van den Driessche, Pauline 19. Velasco-Hernandez, Jorge 20. Wu, Jianhong

3 3 A.1 Agusto, Folashade Chapter A: Participant Contributions 1. The interesting question that has come up during my model formulation is how to capture and model the feedback from the population level model into the within-host model in order to address the issue of the impact of the population level on this two level models. 2. How can this complex system be studied? 3. What are the possible analysis that can be carried out on this model both from the mathematical stand point as well as from the ecological and evolutionary stand point? 4. What are the numerical tools that can be used for the system bifurcation analysis and for parameter estimation? 5. On the issue of parameter estimation, how can the feedback parameter be estimated? Given that in most cases data exist for both models(with-in and between models) in isolation. A.2 Baez, Javier I am mainly interested in the interaction of cancer and the immune system. A.3 Belair, Jacques My epidemiological interest is in mosquito-borne diseases, and in particular in the propagation of Dengue Fever and the role played in it by resource allocation (restrictions to a subgroup, hospital-bed limitation) and exposure to the different serotypes (waning and cross immunities). The mechanisms of infection appear to be convoluted, and symptoms of hematological pathologies (thrompocytopenia in particular) accompany it. Since I have spent some time on modeling formation and dysregulation of blood cells, I would like to see how these in-host mechanisms determine, as a function of time, crossimmunity. REFERENCES: Tsai, J.J., Lui, L.T. et al. (2011) The importance of hematopoietic progenitor cells in dengue. Ther. Adv. Hemat. 3 (1): Halstead, S.B. (2007) Dengue. Lancet 370: Martine, B.E. Koraka, P. and Osterhaus, A.D. (2009) Dengue virus pathogenesis: an integrated view. Microbiol Rev 22: WHO (2010) report of the meeting of the WHO/VMI Workshop on Dengue modeling. WHO/IVB/11.02 Perng, G.C (2012) Role of bone marrow in pathogenesis of viral infections. J. Bone Marrow Res. doi: / A.4 Childs, Lauren Topics of interest in immuno-epidemiology: - How will intervention and eradication strategies for malaria need to change as the prevalence drops and individuals no longer retain immunity to disease? - How would a malaria vaccine intended to prevent severe disease of individuals impact the overall prevalence of malaria?

4 4 - Can signatures of antibody dependent enhancement in dengue virus infection be observed at a population level? - How will vaccination against dengue virus, in particular against particular subtypes, alter the distribution of dengue in general and serotypes specifically? Expectations for the workshop: - Meet and interact with other researchers in immuno-epidemiology, both theoretical and experimental. - Make substantial progress on a problem of interest to participants. - Establish collaborations with other researches in the field. A.5 Feng, Zhilan Because this is relatively new topic, it is challenging to identify appropriate approaches to linking the epidemiological and immunological processes in a model, while keeping the model as simple as possible. Discussions of modeling ideas in the group would be helpful. A.6 Glasser, John Modeling the reactivation of latent viruses and the potential effect of vaccination. Several viruses establish latency after infecting human hosts, who may experience reactivations after recovering from acute infections. Reactivations may be controlled, as in herpes zoster through middle age, or be asymptomatic in some and symptomatic in others, as in herpes simplex. And people with symptomatic reactivations may be infectious. Women who are infected with cytomegalovirus for the first time or who experience reactivations of latent virus or re-infection with new viral strains during pregnancy may infect their developing fetuses. Consequences of congenital infection include spontaneous abortions, stillbirths and neurological and sensory impairments. Infants may also acquire cytomegalovirus during birth, postnatally via breast milk or from other infants in day care. Most infections acquired postnatally are asymptomatic in healthy full-term infants, but can be severe in premature ones lacking maternal antibodies. While what triggers reactivations is unknown, immunity undoubtedly controls them. Age and pregnancy are immune-compromising conditions. Just as vaccination reduces infections with varicella and reactivations of zoster, vaccinating susceptible women of reproductive age might prevent cytomegalovirus infections and vaccinating infected ones might prevent re-infection or delay reactivation. I m interested in exploring ways in which these potential effects of vaccination could be modeled. A.7 Gulbudak, Hayriye In workshop, the topics I would like to discuss are the drawbacks of immuno-epidemiological modeling, how we can develop it and what mathematical challenges are presented by immunoepidemiological modeling. In general, in immuno-epidemiological models although epidemiological models are depending on the immune dynamics, the other way is not true; i.e immunological models are independent from the epidemiological models. In which case, it may not be a realistic assumption. I would like to discuss how we can construct an immuno-epidemiological model where both immune and epidemiological dynamics are influenced by each other and mathematically it can be analysed. References that might be interesting for other participants of the workshop are:

5 1) Modeling hostparasite coevolution: a nested approach based on mechanistic models by M. Gilchrist and A. Sasaki. 2) Immunoepidemiology bridging the gap between immunology and epidemiology by B. Hellriegel. The benefits I am expecting from participating in this workshop are communicating with other researchers who have the same interest, team working, learning more about the topic, understanding challenges and issues in the topic. A.8 Gumel, Abba My main interest pertains to the design of reasonably good models for assessing the impact of climate change and the use of some pharmaceutical interventions on the withinhost and between-host dynamics of some pathogens (particularly vector-borne diseases). A.9 Heffernan, Jane I have been interested in immuno-epidemiological models for over a decade. I believe that outside pressures on the immune system, and immunity distributions in a population should be considered when studying infectious diseases. I have taken some time to model measles in this manner, I am continuing my work on this pathogen, and I am extending my work to include influenza. There are many research questions that I have been pondering in immuno-epidemiology. Topics that we could consider for discussion at this workshop are: - Immuno-epi models using mathematics vs agent based computer simulations - benefits and detriments - Fast and slow timescales in the multiscale problem - When are immuno-epi models needed? For what diseases? A.10 Lenhart, Suzanne I have been working on linking immunology and epidemiological models, using ODEs (within host, with time since infection) linked with first order PDEs and ODEs (between hosts). My recent work in this area involves Johne s disease in dairy cows. It is interesting to understand how the immunology features affect the spread of the disease. I have also been working on optimal control of such systems. Drug treatments may affect the immunology level directly and the spread of the disease indirectly. A.11 Li, Jing At the workshop, I would like to discuss the following topics: 5 What are the current challenges for mathematical modeling and public health in connection with understanding pathogen dynamics within-host and across scales. Which diseases require special attention at the moment concerning understanding the linkage of immunology and epidemiology? What are the currently available modeling tools and techniques to link within-host dynamics to populations-level dynamics? What are the existing gaps between the real-life problems and the current state-ofthe-art tools and techniques for infectious disease management? Categorize the possible tools and techniques in coordination with the biological problems.

6 6 What further tools are needed to fully understand the management of specific diseases? Specific problems in immuno-epidemiology you would like to work during that week I am not sure at the moment yet. However, I would like to identify several biological problems where the link between with-host dynamics and between-host dynamics is needed urgently; identify potential modeling tools and skills which can be used to investigate the above problems; foresee the possible challenges from the modeling perspective; design possible solutions. References that might be interesting for other participants of the workshop Here is a list of the references I found: A. Julia R. Gog, Lorenzo Pellis, James L.N. Wood, Angela R. McLean, Nimalan Arinaminpathy, James O. Lloyd-Smith, Seven challenges in modeling pathogen dynamics within-host and across scales, Epidemics, Volume 10, March 2015, Pages B. Nicole Mideo, Samuel Alizon, Troy Day, Linking within- and between-host dynamics in the evolutionary epidemiology of infectious diseases.trends Ecol. Evol. 23(9), r eturnhttp%3a%2f%2flinkinghub.elsevier.com%2fretrieve%2fpii%2fs % C. Leslie A. Reperant, Thijs Kuiken, Bryan T. Grenfell, Albert D. M. E. Osterhaus, Andrew P. Dobson, Linking Influenza Virus Tissue Tropism to Population-Level Reproductive Fitness.PLoS ONE 7(8), e /journal.pone D. J.M. Heffernan, M.J. Keeling, Implications of vaccination and waning immunity. Proc. R. Soc. B: Biol. Sci. 276(1664), /rspb I guess that some of us might be interested in the special issue of Epidemics: Volume 10, Pages (March 2015) in Modelling Infectious DIsease Dynamics What do you expect from the week at AIM From the week at AIM, I expect: to find some specific problems to work on; to form new collaboration(s). A.12 Magpantay, Felicia Maria I am highly interested in working on the following topics: 1. Mathematics of imperfect vaccines: honeymoon periods and resurgence 2. State-dependent delay differential equations for structured populations 3. Statistical inference methods (iterated filtering, sequential Monte Carlo) 4. Age-structured versus unstructured dynamics of diseases. How this affects our estimates of parameters.

7 A.13 Numfor, Eric I would like the following to be discussed at the workshop: - Immuno-epidemiology for the spread of viral infections in network populations - Relationship between within-host immune escape and between-host infectiousness/virulence in HIV and malaria. During the workshop at AIM, I will expect to: - learn more on the immunology and epidemiology of some infectious diseases - learn other methods of coupling immunology and epidemiology models - have a productive workshop that results in a collaboration. A.14 Pell, Bruce Topics that I would like to see discussed Do nested models give new insights that within-host models and population scale disease models do not? How to model population disease dynamics with influence from within-host dynamics. Ecological stoichiometry applied to within-host pathogen dynamics. General pathways and mechanisms that math models should incorporate for immune system modelling. Specific questions What individual traits and mechanisms are also relevant at the population level for disease dynamics? How do we incorporate these mechanisms or develop their functional forms so we may use them in models at the population scale. How do intracellular nutrients influence virus and host immune fitness and how can we link this to population scale dynamics? Papers of interests S. L. Aalta et al. A three-way perspective of stoichiometric changes on host-parasite interactions. Trends Parasitol., pages N. Mideo et al. Linking within-and between-host dynamics in the evolutionary epidemiology of infectious diseases. Trends in ecology & evolution. 23(9): , 2008 V. Smith. Host resource supplies influence the dynamics and outcome of infectious disease. Integr. Comp. Biol., 47(2): , 2007 V. Smith et al. Host nutrition and infectious disease: An ecological view. Font. Ecol. Environ., 3(5): , 2005 More on ecological stoichiometry and within-host pathogen dynamics Host and host cells, like all things, are made up of elemental compositions. In particular, elements like phosphorus, carbon and nitrogen are fundamental to major biomolecules such as nucleic acids and amino acids. These same nutrients and elements are resources not only for pathogens/viruses, but the host immune system. That is, parasite and host fitness can be linked to the nutrient ratio within the host. Recently, many scientific papers have 7

8 8 been written about this and more field/lab experiments are being done, yielding quality data for analysis and model validation. This could be a good starting point for developing new models to aid in understanding and untangling the complex mechanisms and feedbacks of the immune system. A promising framework that allows for mathematical modeling in this direction is ecological stoichiometry. A great review is given by Aalta et al., that links within-host dynamics, host population dynamics and host community dynamics together. What I hope to get out of the workshop New network to facilitate research. New techniques for comparing two different models against data. New techniques for mathematical model analysis. A better understanding of who is doing what in the literature. A.15 Perelson, Alan I would like to discuss multiscale models of viral infection and treatment in which events inside of infected cells are modeled as well spread of virus among cells. Models can be formulated in various ways, ODEs, age-structured PDEs, agent-based, etc. Each has strengths and weaknesses that will be discussed. Estimating parameters from experimental data is challenging but necessary to make practical contributions. I will discuss concrete examples from hepatitis C virus and HIV infection modeling. In addition, if time permits I would like to discuss new work done with Jessica Conway on modeling a phenomenon called post-treatment control of HIV in which patients who initiated antiretroviral therapy during acute infection, remained on therapy for at least a year and then stopped therapy, were able to maintain virus at undetectable (, 50 HIV RNA copies/ml) for years in the absence of therapy. The model is nonlinear and exhibits bistability in some parameter ranges. It provides testable predictions and can be the basis for future modeling work. The basic model is described in Conway, J. and Perelson, A. S. PNAS 112: (2015). A.16 Pugliese, Andrea I believe that some general questions worth discussing are : - which kind of immuno-epidemiological models have been considered so far? - beyond the interesting mathematics, which are the biological insights learnt from these models? - which are interesting problems to approach? Being more specific, I think we can distinguish between models where within-host dynamics (immune-pathogen interactions) is modelled to detail the process of infection, and models focussed on immunity decay and boosting. An example of the first kind is in my recent paper with Gandolfi and Sinisgalli1, on of the second is the paper by Barbarossa and Röst 2. In models concerning the dynamics of the infection process is independent of epidemic dynamics at the population level, and such models could also be described as age-structured or stage-structured epidemic models. Consideration of within-host processes has been fundamental for evolutionary questions3, and might help in obtaining realistic profiles of infectiousness vs. infection-age, and in understanding better phenomena like vaccination failure. Related questions can be:

9 - are their infections (I understand that a lot of information should exist about HIV, but I know very little) where a within-host model has been obtained which is both realistic and simple enough to be usefully incorporated in an immuno-epidemiological model? - are there results where the qualitative behaviour of such a model has been established? For instance, there are several age-structured epidemic models whose solutions converge to an equilibrium or to a periodic solution, depending on the infectiousness profile; for instance, it may in principle happen that equilibrium stability is certain infectiousness results from a within-host model. - Are there interesting reasons and tractable models in which within-host processes and infection dynamics interact both ways (for instance through inoculum size, or reinfection in the initial infection stages). Some questions concerning models centred on the dynamics of immunity: - in the framework of the model by Barbarossa and Röst, infections are all or none. Would it instead be useful considering partial immunity, so that individuals with a low immune level can actually get infected, although with a lower level of infectiousness? - can immune-epidemiological models help in our understanding of diseases like varicellazoster, where it has been hypothesized for several years that contact with infectious individuals boosts the immune system and reduces the zoster risk. A recent paper4 is based on this assumption and fits it to data, using an ad-hoc form for the boosting effect. Can the data be interpreted also on the basis of a more mechanistic model? - Multi-strain influenza models are often based on assumptions about partial immunity. In such cases, a multi-dimensional immune space seems clearly needed. Could this be incorporated into sensible and tractable models? References 1. Gandolfi, A., Pugliese, A. and Sinisgalli, C. (2015). Epidemic dynamics and host immune response: a nested approach, J Math Biol. 70: M. V. Barbarossa G. Rst (2015). Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting. J. Math. Biol. (in press), DOI /s Gilchrist M, Sasaki A (2002) Modeling host-parasite coevolution. J Theor Biol 218: G Guzzetta, P Poletti, E Del Fava, M Ajelli, GP Scalia Tomba (2013) Hope- Simpson s Progressive Immunity Hypothesis as a Possible Explanation for Herpes Zoster Incidence Data, American journal of Epidemiology 177: I expect from the week to learn about some new progress that have been made, to see some new viewpoints on these problems, and hopefully to start some new collaboration on related problems. A.17 Thieme, Horst I expect from the workshop a rigorous derivation of the mathematical models. Actually, I am somewhat skeptical that this can done. Models that I have seen in the literature so far do not seem to be well founded except those for worm diseases where parasite loads can be counted in discrete units. 9

10 10 I have thought about linking in-host dynamics and spread of infection since 30 years, but did not come up with something sensible. The closest I got is joint work with a former Ph.D. student of mine. Thieme, Horst R.; Yang, Jinling; An endemic model with variable re-infection rate and applications to influenza. John A. Jacquez memorial volume. Math. Biosci. 180 (2002), D30 (35F30 37N25 47H20 92C50) A.18 van den Driessche, Pauline My research in the scope of this workshop has been in mathematical epidemiology, so I am very interested in learning about mathematical immunology, and how the two areas can be combined into mathematical immuno-epidemiology. In particular, I would like to learn about and make progress on the following items: For a particular diseases, how to use results from mathematical immunology to estimate parameters to feed into models in epidemiology. Use of the mathematical tools developed in mathematical epidemiology to analyze models in mathematical immunology. Development of mathematical tools specific to models in immunology. The challenges in combining these two areas, and questions that are important in the control of infectious diseases. A.19 Velasco-Hernandez, Jorge I am interested in the mathematical modeling of infectious diseases both as a tool of public health policy and also as a theoretical endevour. My work has centered in the modelling of Dengue, Chikungunya and respiratory infections on the applied side. On the thoretical one, I am interested in extending the ideas of metapopulation theory to other fields, for example, the modeling of within-host bewteen-host dynamics, the modeling of innovation spread, and some more technical issues as parameter estimation are recent fields of interest A.20 Wu, Jianhong I am particularly interested how in-host information can be incorporated into an epidemiological system to predict treatment outcome at the population level. I would like to see selective examples where biological details can be simplified so mathematical formulation is theoretical trackable for qualitative insights.