[Population Modeling] Amit Huppert's population dynamics overview

[amit Huppert]

In recent years, there has been a growing interest on how to employ data,
combined with population modeling, with the aim to address some of the
important biological questions regarding the population dynamics in a more
realistic way. An especially promising approach, which also raises
methodological challenges, is to develop methods to improve our ability of
combining different types of data sets, each with its own unique features,
in order to piece together a faithful portrait of the underlying forces,
which govern the dynamical processes. Two classical examples that we have
been studying in recent years are i) the unfolding of epidemics ii)
predator prey interactions. In the case of infectious disease outbreaks the
goal is to utilize data in order to first estimate the model parameters and
conduct model selection. In the second phase, the selected model can be
used to study different control methods with the aim of reducing and/or
curtailing the outbreak in an optimal way (Yaari et al).  When studying
ecological interactions there are many myriad theoretical studies that
explore the role of spatial structures on predation and/or competition
among different organisms. However, there are only sparse field studies
that have validated, and quantified their predictions. In our work (Dattner
et al), we combine experimental results, which observed the temporal
dynamic of the predatory bacterium, and its prey, in a structured
environment composed of sand under various regimes of water content. By
constructing a dynamic model, and estimated its parameters. The ability of
the model to fit the data combined with realistic parameter estimates
indicate that bacterial predation in the sand can be described by a
relatively simple model, and stress the importance of prey refuge on
predation dynamics in heterogeneous environments.



Mathematical models are a vital tool, which can be used to resolve complex
biological phenomena such as multihost transmission. Yet, theoretical
studies on multihost diseases are sparse.  We developed and analyzed a set
of novel dynamic models (Miller et al). The modeling framework is based on
that of Ross, which was extended to include two distinct host species, one
vector species with variable preferences, and unlike previous studies, a
critical separation between density and diversity parameters (richness and
evenness). The model analysis reveals a new mechanism for disease
amplification. In this mechanism the maximum disease risk is obtained when
both host species are present in the community. The model expands on the
previous understanding about the relationship between host diversity and
disease risk by formulating the exact conditions under which diversity
amplification, or dilution, would occur. Such formulation is able to
account for the different and contradictory patterns often observed in
nature. We have also extended the model to look at personal protection (PP)
techniques, such as insecticide treated nets (ITN), repellents, and
medications, include some of the most important and commonest ways used
today to protect individuals from vector borne infectious diseases.  To
this end, a dynamic model was developed which incorporates parameters that
describe the potential effects of PP on vector searching and biting
behavior and calculated its basic reproductive rate, *R0*. The model
analysis revealed that partial coverage with popular PP techniques can
realistically lead to a substantial increase in the reproductive number. An
increase in *R0* implies an increase in disease burden and difficulties in
eradication efforts within certain parameter regimes.  Such findings
therefore stress the importance of studying vector behavioral patterns in
response to PP interventions for future mitigation of vector borne
diseases.





*References *



Miller E and Huppert A. The effects of host diversity on vector-borne
disease: The conditions under which diversity will amplify or dilute the
disease risk. PLoS ONE 8(11): e80279. doi:10.1371/journal.pone.0080279



Miller E, Dushoff J, and Huppert A. The risk of incomplete personal
protection in vector borne disease Journal of The Royal Society
Interface 13.115 (2016): 20150666.‏



Yaari R, Katriel G, Stone L, Mendelson E, Mandelboim M, Huppert A. 2016
Model-based reconstruction of an epidemic using multiple datasets:
understanding influenza A/H1N1 pandemic dynamics in Israel. Journal of The
Royal Society Interface  13: 20160099.
http://dx.doi.org/10.1098/rsif.2016.009



Rami Yaari, Ehud Kaliner, Itamar Grotto, Guy Katriel ,Jacob Moran-Gilad,
Danit Sofer,  Ella Mendelson, Elizabeth Miller and Amit Huppert.  Modeling
the spread of polio in an IPV-vaccinated population; lessons learned from
the 2013 silent outbreak in southern Israel. BMC medicine 14.1 (2016): 95.



Dattner, I., Miller, E., Petrenko, M., Kadouri, D. E., Jurkevitch, E., &
Huppert, A. (2017). Modelling and parameter inference of predator–prey
dynamics in heterogeneous environments using the direct integral
approach. Journal of The Royal Society Interface, 14(126), 20160525.
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