Investigating heterogeneity in the dynamics of virus and immune response following a yellow fever vaccination Open Access

Jia, Johnathan Dexuan (2015)

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A key feature of the dynamics of infection in humans is that different individuals form different responses to a given pathogen. This has been demonstrated in recent studies conducted by Akondy et al. (2015) following immunization of the yellow fever vaccine. Their results show that there is a 104 fold variation in the peak viral titer and 102 fold variation in the peak immune cell density among human participants. We used simple mathematical models of the within host dynamics of infection to investigate what gives rise to variation between individuals in the dynamics of infection and immunity. We found that changes in most parameters over biologically reasonable ranges resulted in greater changes in peak viral load compared to the peak immune cell density. Only changes in the killing rate of adaptive immunity resulted in similar changes in the peak viral load and peak immune cell density. Our simple model does not recapitulate the yellow fever vaccination data. This indicates that our model assumptions are incorrect. Since our model is the simplest case, we must have failed to consider an important process or factor that would be necessary to recapitulate the observed variation in the yellow fever vaccination data. However our model makes predictions which can be experimentally tested, and in doing so it sets the stage for a quantitative understanding of what gives rise to heterogeneity in the responses of different individuals and infection.

Table of Contents

Abstract pg. 1

Background pg. 2

The Question and the Problem pg. 2

Sources of Heterogeneity pg. 5

How do genetic factors impact the within-host dynamics of infection? pg. 6

How do environmental factors impact the dynamics of infection within a host? pg. 7

How does pathogen heterogeneity affect the immune response? pg. 8

How do other heterogeneous factors influence the dynamics of an acute infection? pg. 9

Our Approach pg. 9

Model pg. 10

Model Schematic pg. 10

Assumptions pg. 11

Model Equations pg. 11

Parameterization pg. 12


Variation in Viral Growth Rate: r pg. 16

Variation in Immune Growth Rate: s pg. 17

Variation in the Pathogen Density at which Immunity Responds: φ pg. 18

Variation in the Rate of Killing of Pathogen by Adaptive Immunity: k pg. 19

Variation in the Initial Viral Load: V(0) pg. 20

Variation in Initial Immunity: X(0) pg. 21

Summarization of the Results pg. 22

Discussion pg. 23

Viral Growth Rate pg. 23

Immune Growth Rate pg. 24

Pathogen Density at which Immunity Responds pg. 25

Killing Rate by Adaptive Immunity pg. 25

Initial Viral Inoculum pg. 26

Initial Immunity pg. 27

Summary: The Questions Revisited pg. 27

Limitations and Future Directions pg. 30

References pg. 31

Appendix pg. 34

Code pg. 34

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