Here we discuss briefly the overall idea of taking a model
perspective, sometimes also called interchangeably a *systems*
perspective, and how it is applied to immune response modeling.

- Understand the basic ideas of complex systems and systems thinking/modeling
- Assess strength and weaknesses of different modeling approaches
- Know the difference between phenomenological and mechanistic models

The scientific approach that has generally been the most successful
in the past was to break down a system into its components and study the
components one at a time. Usually referred to as the *reductionistic
approach*. This approach to understanding the world is still very
powerful and useful.

A complementary approach, which has seen increased use, is to look at
“the whole” system at once, instead of each component at a time. Using
the whole system approach can provide insights that might not be
obtained by the purely reductionist approach. Looking at the whole
system at once is often referred to as *systems
thinking/approach*.

The term *systems thinking* or *systems approach* or
similar such terminology has become popular in various fields during the
last few decades. It is not a very clearly defined term, but in general,
a *systems* perspective looks at multiple - often many -
components that interact with each other in potentially complicated
ways. Since models are an indispensable tool to study system of
interacting components, the term *model thinking* is also
sometimes used. More generally a systems perspective and the use of
models generally go together.

In the context of within-host infection and immunology, the system is
the complex interactions of pathogen, host, and possibly environment,
that determine the process and outcome of an infection. Since infections
unfold over time, we usually want to study the *dynamics* of our
system. This leads us to a *dynamical systems perspective*.
Specific types of models, called *mechanistic models* are
especially well suited to describe dynamical systems and are therefore
the primary choice for the study of complex dynamical systems. We
describe them next.

Models are everywhere in science. Models can be conceptual (e.g. graphs or charts), experimental model systems (e.g. a specific mouse strain in immunology) or take the form of mathematical/computer models. The terms ‘model’ and ‘modeling’ are widely used and have no clearly defined meaning. We start by defining and distinguishing between 2 broad categories of models and then focus in the following on one of them.

Once we take the systems perspective, we have to deal with many
components that interact in potentially complicated ways. Making study
and analysis complicated, especially if we are trying to gain insights
into the causal and mechanistic connections between some quantity
(exposure) and some outcome. When taking a systems approach, it is
therefore often not enough to have a conceptual model alone. While a
conceptual approach often allows some qualitative understanding, it is
somewhat limiting. It is for instance almost impossible to gain a good
*quantitative* understanding how changes in certain conditions
and components of a system lead to changes in outcomes of interest by
relying on conceptual approaches alone. If we want to go beyond
qualitative and move toward a quantitative understanding, we need
mathematical/computational models. There are many different types of
models one can implement. The following categorizes and defines two
major types of modeling approaches. In this couse, we will focus on the
second type of models.

A huge class of models consists of what we usually refer to as
statistical models. In the context of this discussion, I prefer to label
them *phenomenological* models, but that terminology is rarely
used. The idea behind the phenomenological approach is to build a
parsimonious mathematical or computational model and use statistical
approaches to compare the model with the data and to determine if there
are any patterns in the data.

For instance, a linear regression model investigates if there is a
pattern/correlation between some input(s) and output(s) of interest that
can be well approximated by a linear function. More complicated
statistical models exist, some go by the name of *machine learning
methods*. All of these models try to determine if there are patterns
between inputs and outputs of interest in the data. Statistical
methodology can then be used to determine if any observed pattern is
“real” or might be due to chance. The simple t-test is an example.

These phenomenological models do not try to describe the mechanisms by which patterns might arise. For instance, if we find that the number of T-cells at the peak of an infection correlates linearly with the number of epitope-specific naive T-cells, we can’t conclude for certain that the precursor number of T-cells is the cause of different peak T-cells (though it is a reasonable assumption). We also do not know what processes and mechanisms lead from naive T-cells to activated T-cells.

This non-mechanistic, phebomenological approach is both a strength
and a weakness. With this approach, we can find patterns
(e.g. correlations) in data without having to be able to postulate
mechanistically how those patterns arise. On the flip side, these
phenomenological models also provide little insight regarding potential
mechanisms. If we want to explicitly study mechanisms and processes
using models, we need to use *mechanistic* models, described
next.

As the name suggests, mechanistic models try to explicitly model the mechanisms leading to observed patterns for a given systen under study. Usually, the models are a highly simplified - but done well, still very powerful - abstraction of the system under study. The advantage of these kinds of models is that they potentially provide mechanistic insights, leading to a better and deeper understanding of the system. The main disadvantage is that we already need to know (or at least assume) a good bit about how the components interact for us to be able to build such a model. If we don’t know enough to even postulate potential mechanisms underlying the observed data, we can’t build a mechanistic model.

Mechanistic models are generally evaluated with computer simulations, thus in this course we mostly refer to them as simulation models. While this terminology is a bit fuzzy (e.g. complex statistical/phenomenological models often also rely on simluations), for the purpose of this course all our models are mechanistic simulation models and we use either term.

Both phenomenological and mechanistic models are useful tools with distinct advantages and disadvantages. Deciding which one to use depends on the question and study system. Here, we will focus our discussion on mechanistic models. Since the most common type of mechanistic model in the context of within-host modeling are ordinary differential equation based models, we will focus on those, with a brief mention of other mechanistic modeling approaches.

Early mechanistic models for the immune response, with a focus on B-cells, were developed in the 70s (see e.g. (Bell 1970, 1971b, 1971a)). An early, semi-mechanistic model to describe influenza infections was developed in (Larson et al. 1976). The use of such mechanistic models to study infection and immune responses dynamics continued to slowly increase during the 70s and 80s, and really took off in the 90s. Mechanistic models played an important role in understanding HIV infection dynamics and treatment (Ho et al. 1995; Perelson et al. 1996), and have since been applied to many other infectious diseases such as HCV (Neumann et al. 1998), malaria (Mideo, Day, and Read 2008), tuberculosis (Wigginton and Kirschner 2001) and many others.

The paper “Why Model?” by Joshua Epstein (Epstein 2008) provides a nice, short discussion of the purposes of models. Other general introductory discussions of systems thinking and model use are (May 2004; Chubb and Jacobsen 2010; Garnett et al. 2011; Basu and Andrews 2013; Gunawardena 2014; Homer and Hirsch 2006; Peters 2014; Sterman 2006).

Basu, Sanjay, and Jason Andrews. 2013. “Complexity in
Mathematical Models of Public Health Policies:
A Guide for Consumers of
Models.” *PLoS Medicine* 10 (10): e1001540.
https://doi.org/10.1371/journal.pmed.1001540.

Bell, George I. 1970. “Mathematical Model of Clonal Selection and
Antibody Production.” *Journal of Theoretical Biology* 29
(2): 191–232.

———. 1971a. “Mathematical Model of Clonal Selection and Antibody
Production III. The Cellular Basis of
Immunological Paralysis.” *Journal of Theoretical Biology*
33 (2): 379–98.

———. 1971b. “Mathematical Model of Clonal Selection and Antibody
Production. II.” *Journal of Theoretical
Biology* 33 (2): 339–78.

Chubb, Mikayla C., and Kathryn H. Jacobsen. 2010. “Mathematical
Modeling and the Epidemiological Research Process.” *European
Journal of Epidemiology* 25 (1): 13–19. https://doi.org/10.1007/s10654-009-9397-9.

Epstein, Joshua M. 2008. “Why Model?” *Journal of
Artificial Societies and Social Simulation* 11 (4): 12.

Garnett, Geoffrey P., Simon Cousens, Timothy B. Hallett, Richard
Steketee, and Neff Walker. 2011. “Mathematical Models in the
Evaluation of Health Programmes.” *The Lancet* 378 (9790):
515–25.

Gunawardena, Jeremy. 2014. “Models in Biology:‘accurate
Descriptions of Our Pathetic Thinking’.” *BMC
Biology* 12 (1): 29.

Ho, D. D., A. U. Neumann, A. S. Perelson, W. Chen, J. M. Leonard, and M.
Markowitz. 1995. “Rapid Turnover of Plasma Virions and
CD4 Lymphocytes in HIV-1 Infection.”
*Nature* 373 (6510): 123–26. https://doi.org/10.1038/373123a0.

Homer, Jack B., and Gary B. Hirsch. 2006. “System Dynamics
Modeling for Public Health: Background and Opportunities.”
*American Journal of Public Health* 96 (3): 452–58.

Larson, E. W., J. W. Dominik, A. H. Rowberg, and G. A. Higbee. 1976.
“Influenza
Virus Population Dynamics in the Respiratory Tract of Experimentally
Infected Mice.” *Infect Immun* 13 (2): 438–47.

May, R. M. 2004. “Uses and Abuses of
Mathematics in Biology.”
*Science* 303 (5659): 790–93. https://doi.org/10.1126/science.1094442.

Mideo, Nicole, Troy Day, and Andrew F Read. 2008. “Modelling
Malaria Pathogenesis.” *Cell Microbiol* 10 (10): 1947–55.
https://doi.org/10.1111/j.1462-5822.2008.01208.x.

Neumann, A. U., N. P. Lam, H. Dahari, D. R. Gretch, T. E. Wiley, T. J.
Layden, and A. S. Perelson. 1998. “Hepatitis
C Viral Dynamics in Vivo and the Antiviral Efficacy of
Interferon-Alpha Therapy.” *Science* 282 (5386):
103–7.

Perelson, A. S., A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D.
Ho. 1996. “HIV-1
Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and
Viral Generation Time.” *Science* 271 (5255): 1582–86.

Peters, David H. 2014. “The Application of Systems Thinking in
Health: Why Use Systems Thinking?” *Health Research Policy and
Systems* 12 (1): 51.

Sterman, John D. 2006. “Learning from Evidence in a Complex
World.” *American Journal of Public Health* 96 (3):
505–14.

Wigginton, J. E., and D. Kirschner. 2001. “A Model to Predict
Cell-Mediated Immune Regulatory Mechanisms During Human Infection with
Mycobacterium Tuberculosis.” *J Immunol*
166 (3): 1951–67.