The rate at which HIV epidemics rise is determined by transmission
patterns during early HIV infection (1). This six to 12 month
period of high viremia includes both primary infection and the
time when the large pool of latently infected cells built up during
primary infection is being drained. But it is not just the increase
in contagiousness associated with high viremia that gives early
HIV infection its influence. Transmission dynamics can transform
even a small increase in transmission probabilities during this
period into a dominant force. To explain how this occurs, we must
go beyond the simple models of transmission dynamics which Anderson
and May use to derive the formula R0
= cßD (2). (The basic reproduction rate equals the effective
contact rate times the transmission probability per contact times
the duration of contagiousness.) The correctness of this formula
depends upon two untenable assumptions: 1) Infection has a single
stage, and 2) The population mixes randomly. When we relax these
assumptions we see that the single measure of transmission potential,
R0, becomes four different measures
with separate influences on transmission dynamics.
The four measures of transmission potential are N0I,
the individual basic reproduction number, R0I, the
individual basic reproduction rate, N0P, the population
basic reproduction number, and R0P, the population
basic reproduction rate. For a one stage disease in a randomly
mixing population, N0I = R0I = N0P
= R0P = cßD.
N0I is the average number of transmissions from an
infected individual over the course of their infection when everyone
they contact is susceptible. Neither the timing of transmission
nor the type of individuals to whom transmission occurs influence
the value of N0I.
R0I is the rate at which infected individuals would
transmit to others over the course of infection if all of their
contacts were susceptible. While being uninfluenced by the type
of individual to whom transmission occurs, it is influenced by
the timing of when transmission occurs over the course of infection.
For a one stage infection R0I = N0I but
for HIV R0I > N0I.
N0P as defined by Diekmann et al (3) reflects the average
extent to which chains of transmission get amplified across many
generations of transmission. At a value of 1 it determines the
population transmission threshold in models where the contact
rate does not depend upon the availability of partners. When mixing
is completely at random, N0P = N0I. That
is because in random mixing situations an individual generating
a low number of transmissions will transmit to the same group
of people as an individual generating a high number of transmissions.
There will be no preferential connection of high risk individuals.
Given random mixing, the type of individuals who get infected
in one generation of transmission is completely independent of
the type of individuals who got infected in the previous generation
of transmission.
R0P as we use it here reflects the speed at which chains
of transmission get amplified during the early stages of the epidemic
process when everyone contacted is susceptible. We have not formulated
its determinants mathematically but instead equate it with the
early rate of rise of epidemics in numerical solutions of multistage
infection models in non-randomly mixing populations.
To explain why R0I > N0I for HIV, we
consider a two stage disease in a randomly mixing population.
N0I over the total of the two stages is just the number
of transmissions in the early stage plus the number of transmissions
in the late stage. N0I(Tot) = N0I(Early)
+ N0I(Late) = cEßEDE
+ FEcLßLDL where
the E and L subscripts specify parameters relevant to the early
stage or late stage and FE is the fraction of individuals
who survive through the early stage to reach the late stage. Note
that given random mixing the endemic equilibrium of infection
is determined by the N0I(Tot). It does not matter how
much of that number is in the early stage or the late stage. Endemic
equilibrium will be reached when each infected individual is generating
just one other infected individual. That will happen when N0I(Tot)
times the fraction of the population that is susceptible equals
one.
Unlike N0I(Tot), R0I(Tot) will depend upon
how much of the basic reproduction number is apportioned to the
early or the late stage of infection. The more that gets apportioned
to the early stage of the epidemic, the faster the epidemic will
rise to its endemic level. When either contact rates or transmission
probabilities during early infection are higher than they are
during late infection, N0I(Tot) < R0I(Tot).
That means that the epidemic will rise faster than would be predicted
on the basis of the level at which infection levels off.
Because we were viewing HIV transmission dynamics in this context,
the observation of a very fast rising epidemic in the San Francisco
Hepatitis B study cohort which leveled off quickly indicated to
us that N0I < R0I for HIV infection.
In order for the epidemic to have risen as quickly as it did and
then leveled off given this assumption of random mixing, we concluded
that a high proportion of the N0I(Tot) must be in the
N0I(Early). We made this argument in a paper that won
the Howard Temin award as the outstanding epidemiology paper of
1994 (4). But our argument in that paper was too simple. That
is probably why it won an award.
The assumption of random mixing is unrealistic. To be realistic
we have to consider how and why non-random mixing makes the individual
measures of transmission potential differ from the population
measures.
The concentration of transmissibility in early HIV infection that
makes N0I < R0I also makes N0P
< R0P. But the assumption of random mixing intrinsic
to these individual measures is unrealistic. There are important
additional issues of how transmissions between individuals in
different stages of infection get connected to each other across
generations of transmission which make the difference between
N0P and R0P much greater than the difference
between N0I and R0I.. What seem at first
to be rather subtle biases in who transmits to whom across a single
generation of transmission can have very dramatic total effects
when multiple generations of transmission are linked.
The preferential transmission linking of high transmission rate
individuals to other high transmission rate individuals is a powerful
motor for epidemic transmission. Preferential linking during early
infection, however, has dramatically greater effects on the early
rise of epidemic transmission than does preferential linking during
later stages of infection. Compare a preferential linking that
transforms an N0I of 0.8 to an N0P of 2.0.
If this occurs during late infection such that transmissions on
average occur five years after infection, then over a five year
period the infection level will double. On the other hand if this
occurs during early infection such that the average time to transmission
is 3 months, then 20 generations of transmission will have occurred
by five years and the epidemic will have been amplified more than
half a million times as much by five years.
Consider now why it is that individuals in an early stage of infection
are more likely to transmit to those who will have a high likelihood
of transmitting during their early stage of infection. People
do not have a constant rate of contact with the same type of people
over the course of their lives. There are two types of fluctuations
especially worth mentioning. There are age fluctuations and transient
fluctuations. Most people get infected during a period of indiscretion
in their lives when they are making more sexual encounters in
risky environments than during other times in their lives. This
might be a life stage when young people are coupling with other
young people. It might be an even more transient life stage than
youth. It might be a period of relationship instability. It might
be a period of mobility with movement into unsupportive social
environments that provide many sexual outlets. Such mobility might
result in either adventurism or needs for relationship that lower
one's guard. Whatever the sources of fluctuations, when one gets
infected during this period, one is likely to still be in this
period during early HIV infection and likely to move out of it
during later stages of HIV infection. The individuals one encounters
sexually or through needle contact during these periods are also
likely to be in such periods of their own lives. Consequently
the individuals to whom one transmits during this period are in
turn more likely to transmit during early HIV infection than individuals
one encounters during other life stages.
Our simulations of HIV transmission in populations with such fluctuations
show that these can be very powerful determinants of rapid rise
in HIV infection levels in a population which then level off at
a far lower level than would be the case if R0P equaled
N0P.
In summary, early infection plays a key role in the rise of epidemics
because it increases R0P in relation to N0P.
It does this first by shifting the individual N0I to
early infection so that R0I > N0I.. The
effect of this shift is then greatly amplified for the population
measures of transmission potential by preferential linking of
high risk individuals across generations of transmission. Fluctuations
over a lifetime in the rate and riskiness of sexual and needle
contacts cause this preferential linking to be especially strong
during early HIV infection.
The relative difference between R0P and N0P
has important implications for what infection control programs
will be most effective. Where R0P is close to N0P,
there will not be a great advantage in targeting control interventions
to the early stage of infection. Where R0P is greater
than N0P, there will be such an advantage. This effect
is clearly demonstrated in a series of models we examined to evaluate
the potential impact of virus suppressing therapy on HIV transmission
dynamics. Across a wide variety of models, we found that treatment
can effectively slow HIV transmission. But the degree to which
endemic levels of infection could be reduced was wholly dependent
on R0P when N0P was held constant. No matter
what combination of transmission parameters led to reducing R0P,
no matter whether it was behavior change or contact patterns or
transmission probabilities that affected R0P, an increased
level of R0P was associated with increased endemic
level of infection in the presence of a treatment program. Developing
HIV infection detection services that will detect infection in
its early stages will thus have a very important impact on HIV
transmission in a population. We are engaged in developing HIV
surveillance systems that will have this capacity for detection
of infection in its early stages.
1 Koopman JS, Jacquez JA, Simon CP, Foxman B, Pollock S, Barth-Jones D, Adams A, Welch G, Lange K. The Role of Early HIV Infection in the Spread of HIV through Populations, J of Acquired Immune Deficiency Syndromes & Human Retroviruses 1997;14:249-258
2 Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford, England, 1992
3 Diekmann O, Heesterbeek JAP, Metz AJ. On the definition and the calculation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28:365-382 (1990)
4 Jacquez JA, Koopman JS, Simon CP, Longini IM. The role of Primary Infection in Epidemics of HIV Infection in Gay Cohorts. J of Acquired Immune Deficiency Syndromes 1994;7:1169-84