Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models

HIV infection with single strain

In this approach, it is assumed that there is only one strain of HIV that infects the target cells. No additional features such as mutation, super-infection, or co-infection are considered at the within-host scale. We found three models that include only one strain of HIV at the within-host scale (Shen, Xiao & Rong, 2015; Sun et al., 2016; Yeghiazarian, Cumberland & Yang, 2013). An example of the basic dynamics are shown in Table 2, which also assumes that viral shedding rate (s) has negative effect on the viral load (V) within-host (DebRoy & Martcheva, 2008). This model can be modified to include the effects of drug therapy, which affect the viral production rate and the viral infectivity rate (Shen, Xiao & Rong, 2015; Sun et al., 2016; Yeghiazarian, Cumberland & Yang, 2013).

Table 2:

HIV infection with single strain.

Within-host layer of HIV multi-scale model with assumption of single strain HIV infection. The uninfected CD4+ T cells get infected by the free virions and produce HIV virus. CD4+ T cells have the constant reproduction and death rates. HIV induces death rate of infected cells. HIV population increases by production of virus by infected cells, and decreases because of the virus clearance and shedding rate.

Model diagram
Equations
$\frac{dT}{d\tau }=\lambda -kTV-dT$
$\frac{d{T}^{\ast }}{d\tau }=kTV-\left(\mu +d\right)T^{\ast }$
$\frac{dV}{d\tau }=N\left(\mu +d\right)T^{\ast }-\left(c+s\right)V-kTV$
Parameters
λ	Reproduction rate of uninfected cells
k	Infection rate of uninfected cells
d	Natural death rate of uninfected cells
μ	HIV induced death rate of infected cells
N	HIV production by infected cells
s	Shedding rate of virus
c	HIV clearance rate

DOI: 10.7717/peerj.3877/table-2

HIV super-infection

HIV super-infection occurs when individuals infected with a single HIV strain are infected with a second HIV strain. Martcheva and Li included HIV infection with multiple strains in their model, with the assumption of complete competitive exclusion between the strains at the within-host scale. In this context, the strain with the larger reproduction rate becomes dominant. They studied the impact of virulence of different strains on the equilibrium at the individual and population scales (Martcheva & Li, 2013). Table 3 shows the schematic and formulation of this model.

Table 3:

HIV super-infection.

The within-host layer of HIV multi-scale model illustrates the impact of infection with multiple strains of HIV. This model includes the uninfected, infected target CD4+ T cells with different strains, and different strains of free HIV virions. An individual may get infected with drug-resistant and/or drug-susceptible strains. Also, mutations may happen within-host leading to emergence of drug-resistant strains.

Model diagram
Equations
$\frac{dT}{d\tau }=\lambda -k_{i}T{V}_i-dT$
$\frac{d{T}_i}{d\tau }=k_{i}T{V}_i-\left({\mu }_i+d\right)T_i$
$\frac{d{V}_i}{d\tau }=N_i\left({\mu }_i+d\right)T_i-\left(c+s_i\right)V_i-k_{i}T{V}_i$
Parameters
λ	Reproduction rate of uninfected cells
ki	Infection rate of uninfected cells by virus strain i
μi	HIV induced death rate of infected cell with strain i
Ni	HIV Production of virus i by infected cells
si	Shedding rate of virus strain i
d	Natural death rate of uninfected cells
c	HIV clearance rate

DOI: 10.7717/peerj.3877/table-3

HIV drug resistance

Drug resistance can be acquired through mutations of drug-sensitive strains within-host or through direct transmission of drug-resistant strains. Saenz and Bonhoeffer included HIV infection with drug resistant strains in their model, and studied the effects of antiretroviral treatment (ART) on both drug-sensitive and drug-resistant strains (Saenz & Bonhoeffer, 2013). Table 4 shows the schematic and formulation of this model.

Table 4:

HIV drug resistance.

The within-host layer of HIV multi-scale model illustrates the uninfected and infected target CD4+ T cells, including drug-sensitive and drug-resistant strains. Mutations from drug-sensitive to drug-resistant or drug-resistant to drug-sensitive strains are studied in this model, and the impact of treatment is also included.

Model diagram
Equations
$\frac{dT}{d\tau }=\lambda -\left(1-{ϵ}_{rt}\right)k_{s}T{V}_s-\left(1-p_{rt}{ϵ}_{rt}\right)k_{r}T{V}_r-dT$
$\frac{d{T}_s}{d\tau }=\left(1-m_{sr}\right)\left(1-{ϵ}_{rt}\right)k_{s}T{V}_s+m_{rs}\left(1-p_{rt}{ϵ}_{rt}\right)k_{r}T{V}_r-\left(\mu +d\right)T_s$
$\frac{d{T}_r}{d\tau }=m_{sr}\left(1-{ϵ}_{rt}\right)k_{s}T{V}_s+\left(1-m_{rs}\right)\left(1-p_{rt}{ϵ}_{rt}\right)k_{r}T{V}_r-\left(\mu +d\right)T_r$
$\frac{d{V}_s}{d\tau }=\left(1-{ϵ}_{pi}\right)N_s\left(\mu +d\right)T_s-c{V}_s$
$\frac{d{V}_r}{d\tau }=\left(1-p_{pi}{ϵ}_{pi}\right)N_r\left(\mu +d\right)T_r-c{V}_r$
Parameters
λ	Reproduction rate of uninfected cells
ks	Infection rate of uninfected cells by drug-sensitive strain
kr	Infection rate of uninfected cells by drug-resistant strain
d	Natural death rate of uninfected cells
μ	HIV induced death rate of infected cells
c	HIV clearance rate
ϵrt	Efficacy of reverse transcriptase inhibitor treatment
ϵpi	Efficacy of protease inhibitor treatment
Vs	Drug sensitive strain of HIV
Vr	Drug resistant strain of HIV
msr	A proportion of infected cells with drug-sensitive strain that produce drug resistant virions
mrs	A proportion of infected cell with drug-resistant strain that produce drug sensitive virions
prt	Relative rate of reverse transcriptase inhibitor efficacy for drug resistant strain
ppi	Relative rate of protease inhibitor efficacy for drug resistant strain
Ns	Reproduction of HIV virus by drug-sensitive strain
Nr	Reproduction of HIV virus by drug-resistant strain

DOI: 10.7717/peerj.3877/table-4

HIV evolution

Studies have modeled HIV viral evolution within-host and its impact on transmission between hosts (Lythgoe, Pellis & Fraser, 2013; Doekes, Fraser & Lythgoe, 2017). They investigate the trade-off between increased virus replication and virulence and decrease in virus transmission. Doekes, Fraser & Lythgoe (2017) also included long-lived reservoirs of latently infected CD4+ T cells to determine their impact on HIV within-host competition.

HIV co-infection

HIV co-infection with sexually transmitted infections among high risk groups (Abu-Raddad et al., 2008), and/or co-infection with endemic infections such as malaria (Cuadros et al., 2011) have direct impact on increasing the transmission rate of both infections. Cuadros and García-Ramos incorporated HIV co-infection dynamics in the within-host immune model (Callaway & Perelson, 2002; Stafford et al., 2000; Nowak & May, 2000) to address increased immune response and increased risk of transmission, and evaluated their impact on HIV epidemics (Cuadros & García-Ramos, 2012). Table 5 shows the schematic and formulation of this model.

Table 5:

HIV co-infection.

The within-host layer of HIV multi-scale model illustrates the impact of co-infection. This model includes the uninfected and infected target CD4+ T cells, and free virions. Co-infection increases immune response and the infection rate of immune cells. Therefore, the set-point viral load is higher compared to the case of no co-infection.

Model diagram
Equations
$\frac{dT}{d\tau }=\lambda -kTV-dT+\left[1-\frac{T_m+T+T^{\ast }}{T_{max}}\right]r_{T}T$
$\frac{d{T}^{\ast }}{d\tau }=kTV-\left(\mu +d\right)T^{\ast }+k_{Tm}V{T}_m$
$\frac{dV}{d\tau }=N\left(\mu +d\right)T^{\ast }-cV$
Parameters
λ	Reproduction rate of uninfected cells
k	Infection rate of uninfected cells
d	Natural death rate of uninfected cells
μ	HIV induced death rate of infected cells
N	HIV production by infected cells
c	HIV clearance rate
Tm	Activated immune cells against co-infection
Tmax	Maximum number of immune cells
rT	Growth rate of non-specific immune cells
kTm	Infection rate of co-infection

DOI: 10.7717/peerj.3877/table-5

HIV and therapeutic interfering particles

Therapeutic interfering particles (TIPs) are an emerging drug therapy where therapeutic versions of the pathogen are manufactured to attack viral replication processes and can be transmitted between hosts (Metzger, Lloyd-Smith & Weinberger, 2011). In the within-host model developed by Metzger et al. HIV and TIPs are treated as separate viral strains. The model includes CD4+ T cells infected with HIV only, CD4+ T cells infected with TIPs only, and CD4+ T cells dually infected with HIV and TIPs (Metzger, Lloyd-Smith & Weinberger, 2011).

Acute, latent and late stages of HIV infection

Previous studies have shown that transmission rates differ depending on whether the infected population is in the acute, latent, or AIDS stages (Hollingsworth, Anderson & Fraser, 2008). This conclusion can be incorporated into immunoepidemiological models by categorizing the infected population into different stages (Cuadros & García-Ramos, 2012; Yeghiazarian, Cumberland & Yang, 2013; Sun et al., 2016; Shen, Xiao & Rong, 2015; Saenz & Bonhoeffer, 2013). Cuadros and García-Ramos extended the model so that the HIV+ sub-populations also differed by sexual-risk activity (Cuadros & García-Ramos, 2012). Yeghiazarian et al. divided the infected population into stages to evaluate the timing of treatment initiation at the individual level, and its impact on HIV transmission at the population level. They assumed treatment initiation can start during any stage of HIV infection after diagnosis (Yeghiazarian, Cumberland & Yang, 2013).

HIV super-infection

HIV infected individuals are categorized based on the strains of infection. Due to the assumption of competitive exclusion at the within-host level in the model developed by Martcheva and Li, susceptible individuals only become infected with one of the strains. Thus, only infected individuals having the dominant within-host strain can super-infect individuals with the lesser within-host strain (Martcheva & Li, 2013).

HIV drug resistance

Drug-resistant strains can emerge during antiretroviral therapy (ART) (Rong, Feng & Perelson, 2007), or can be transmitted between individuals who have never been exposed to ART (Hué et al., 2009), which may lead to treatment failure if ART is begun (Hamers et al., 2011). Saenz and Bonhoeffer thus categorize the infected population into those with only drug-sensitive or only drug-resistant strains with or without treatment, and those with drug-sensitive strains that develop drug-resistance while receiving treatment (Saenz & Bonhoeffer, 2013). Table 7 shows the schematic and formulation of this model.

Table 7:

HIV drug resistance and treatment impact.

HIV transmission dynamics between drug-sensitive and drug-resistant infected individuals are illustrated. Infected individuals may get infected by the drug-sensitive or drug-resistant strains. A proportion p of infected individuals get treatment, and among the infected individuals with drug-sensitive strains, a proportion q of them develop drug resistance.

Model diagram
Equations
$\frac{dS}{dt}=b-{\beta }_{DR}S{I}_{DR}-{\beta }_{DS}S{I}_{DS}-\delta S$
$\frac{d{I}_{DR0}}{dt}=\left(1-p\right){\beta }_{DR}S{I}_{DR}-\left(\alpha +\delta \right)I_{DR0}$
$\frac{d{I}_{DRT}}{dt}=p{\beta }_{DR}S{I}_{DR}-\left(\alpha +\delta \right)I_{DRT}$
$\frac{d{I}_{DS0}}{dt}=\left(1-p\right){\beta }_{DS}S{I}_{DS}-\left(\alpha +\delta \right)I_{DS0}$
$\frac{d{I}_{DST}}{dt}=p\left(1-q\right){\beta }_{DS}S{I}_{DS}-\left(\alpha +\delta \right)I_{DST}$
$\frac{d{I}_{DSTr}}{dt}=pq{\beta }_{DS}S{I}_{DS}-\left(\alpha +\delta \right)I_{DSTr}$
Parameters
b	Natural birth rate in the population
IDR0	Number of individuals infected with drug-resistant strain and do not receive treatment
IDRT	Number of individuals infected with drug-resistant strain and receive treatment
IDS0	Number of individuals infected with drug-sensitive strain and do not receive treatment
IDST	Number of individuals infected with drug-sensitive strain and receive treatment
IDSTr	Number of individuals infected with drug-sensitive strain, receive treatment, and develop resistance
βDR	Drug-resistant HIV transmission rate in the population
βDS	Drug-sensitive HIV transmission rate in the population
α	HIV induced mortality rate
δ	Natural death rate in the population
p	Proportion of infected individuals who receive treatment
q	Proportion of infected individuals who receive treatment and develop resistance
IDR	IDR0 + IDRT
IDS	IDS0 + IDST + IDSTr

DOI: 10.7717/peerj.3877/table-7

HIV evolution

Depending on virulence of the strain, infected individuals are categorized by the strain with which they initially became infected (Doekes, Fraser & Lythgoe, 2017; Lythgoe, Pellis & Fraser, 2013). Because it is assumed that all other strains develop from an initial strain and only the most virulent strain is transmitted, infected individuals can end up infecting others with a different strain than they were initially infected. Table 8 shows the schematic and formulation of this model.

HIV and therapeutic interfering particles

The infected population is divided into classes of those infected with HIV only, those infected with Therapeutic Interfering Particles (TIPs) only, and those infected dually with HIV and TIPs. The infected population is also divided into these classes during different stages of infection (Metzger, Lloyd-Smith & Weinberger, 2011). Table 9 shows the schematic and formulation of this model.

Table 8:

HIV evolution.

HIV transmission dynamics between infected individuals with different strains are illustrated. Infected individuals with strains i may get infected with another strain j and transmit the dominant strain of HIV.

Model diagram
Equations
$S\left(t\right)=b-{\sum }_{i=1}^n{\int }_0^{T_i}{H}_i\left(t-\tau \right)e^{-\delta \tau }d\tau$
$I_i\left(t\right)={\int }_0^{T_i}{H}_i\left(t-\tau \right)e^{-\delta \tau }d\tau -\left(\alpha +\delta \right)I_i$
$H_i\left(t\right)=\frac{S\left(t\right)}{N\left(t\right)}{\sum }_{j=1}^n{\int }_0^{T_i}{\beta }_{ij}\left(\tau \right)H_j\left(t-\tau \right)e^{-\delta \tau }d\tau$
Parameters
b	Natural birth rate in the population
Ti	Time of death after initiation of infection
Hi	The rate at which new type-i infection occurs
δ	Natural mortality rate
Ii	Number of individuals infected with strain i
βij	Infectivity of strain i in a host originally infected with strain j at time τ since infection.

DOI: 10.7717/peerj.3877/table-8

Table 9:

HIV and therapeutic interfering particles (TIPs).

HIV transmission dynamics between infected individuals with wild type of HIV and TIPs are illustrated. Individuals can get infected with wild type of HIV, TIPS, or both. Infected individuals can get reinfected with both types.

Model diagram
Equations
$\frac{dS}{dt}=b-{\beta }_W^{I}SI-{\beta }_W^{I_d}\left(1-{\beta }_T^{I_d}\right)S{I}_d-{\beta }_W^{I_d}{\beta }_T^{I_d}S{I}_d-{\beta }_T^{I_d}\left(1-{\beta }_W^{I_d}\right)S{I}_d-\delta S$
$\frac{dI}{dt}={\beta }_W^{I}SI+{\beta }_W^{I_d}\left(1-{\beta }_T^{I_d}\right)S{I}_d-{\beta }_T^{I_d}I{I}_d-\left(\alpha +\delta \right)I$
$\frac{d{I}_d}{dt}={\beta }_W^{I_d}{\beta }_T^{I_d}S{I}_d+{\beta }_W^I{S}_{T}I+{\beta }_W^{I_d}{S}_T{I}_d+{\beta }_T^{I_d}I{I}_d-\left(\alpha +\delta \right)I_d$
$\frac{d{S}_T}{dt}={\beta }_T^{I_d}\left(1-{\beta }_W^{I_d}\right)S{I}_d-{\beta }_W^I{S}_{T}I-{\beta }_W^{I_d}{S}_T{I}_d-\left(\alpha +\delta \right)S_T$
Parameters
b	Natural birth rate in the population
I	Number of infected individuals with only the wild type of HIV
Id	Individuals infected with both HIV and TIPs
ST	Individuals infected with only TIPs
${\beta }_W^I$	Transmission rate of wild type HIV from HIV infected individuals
${\beta }_W^{I_d}$	Transmission rate of wild type HIV from dually infected individuals
${\beta }_T^{I_d}$	Transmission rate of TIPs from dually infected individuals

DOI: 10.7717/peerj.3877/table-9

HIV transmission rate as a function of viral load

The within-host and between-host scales of HIV immunoepidemiological models are coupled by basing the transmission rate on the time-varying viral load since infection. The viral load (and thus the transmission rate) is high during the acute and late stages of HIV infection while being low during the latent stage (Hollingsworth, Anderson & Fraser, 2008; DebRoy & Martcheva, 2008). Table 10 shows the formulation of this model. Unlike the basic SI epidemiological model that assumes constant transmission rate (β), the between-host model assigns time-varying transmission rate, which is dependent on the non-linear viral immune dynamics of HIV in the within-host model.

In some models, the transmission rate depends on the viral load continuously over time (Shen, Xiao & Rong, 2015; Martcheva & Li, 2013; Saenz & Bonhoeffer, 2013). Saenz and Bonhoeffer also distinguished between drug-resistant and drug-sensitive strains and their corresponding impact on the transmission rate (Saenz & Bonhoeffer, 2013). Martcheva and Li made the death of infected individuals depend on the viral load over time, since the AIDS stage is associated with high viral load (Martcheva & Li, 2013).

In the context of HIV evolution, while the transmission rate varies through time depending on the viral load, the viral load is also modeled to distinguish between different strains (Doekes, Fraser & Lythgoe, 2017; Lythgoe, Pellis & Fraser, 2013). The transmission rate depends on a predefined infectivity profile which changes depending on the stage of infection, and the frequency of the different viral strains in an infected population. Doekes et al. made the transmission rate depend on the frequency of viral strains that were only in actively infected CD4+ T cells (Doekes, Fraser & Lythgoe, 2017).

The within-host viral load can be used to individualize the transmission rate over time (Yeghiazarian, Cumberland & Yang, 2013; Sun et al., 2016). The CD4+ T cell count can also be used to determine the stage of infection (Yeghiazarian, Cumberland & Yang, 2013).

HIV transmission rate using viral load equilibrium

Another method of linking the within-host and between-host scales is to use the within-host model to determine an equilibrium for the viral load. This equilibrium can then be used as a constant parameter in the between-host model, which can then be analyzed further by differing the parameters of the within-host model (Metzger, Lloyd-Smith & Weinberger, 2011; Cuadros & García-Ramos, 2012). Cuadros & García-Ramos (2012) accounted for the amplified viral load due to co-infection and the corresponding increase in HIV transmission rate. Metzger, Lloyd-Smith & Weinberger (2011) determined the differing viral loads associated with HIV and TIPs, and their effect on the transmission probabilities between infected populations.

HIV virulence

Clinical studies have shown that HIV has evolved an intermediate level of virulence at the within-host level that optimizes the transmission potential of the virus at the population level (Fraser et al., 2007). However, at the within-host level, HIV can evolve quickly (Lemey, Rambaut & Pybus, 2006), virulence increases during the course of the infection (Kouyos et al., 2011), and infections with higher replicative capacities have higher virulence (Kouyos et al., 2011). Replicative capacities also increase over the course of infection, albeit slowly (Kouyos et al., 2011). Because of this behavior of HIV at the within-host level, it might be expected that HIV would evolve a high virulence at the within-host level, even if it did not optimize the transmission potential at the population level. To understand these seemingly contradictory results, immunoepidemiological models were used, which incorporated these behaviors of HIV at the within-host level (Lythgoe, Pellis & Fraser, 2013; Doekes, Fraser & Lythgoe, 2017). The model developed by Lythgoe, Pellis & Fraser (2013) found that small rates of within-host evolution optimize the transmission potential at the population level, whereas higher rates of within-host evolution lead to high levels of virulence, but lower transmission potential. Lythgoe, Pellis & Fraser (2013) suggest that the clinical observations seen in HIV may be a result of a within-host fitness landscape that is complex to traverse, since this leads to smaller rates of within-host evolution. They also suggest the effect of the adaptive immune response may play a role in explaining the observed behavior (Lythgoe, Pellis & Fraser, 2013). Based off the results from Lythgoe et al., a similar model was constructed by Doekes, Fraser & Lythgoe (2017), which included a latent reservoir of CD4+ T cells at the within-host level. They found that this latent reservoir may be responsible for delaying the evolutionary dynamics at the within-host level, which then leads to the transmission potential being optimized (Doekes, Fraser & Lythgoe, 2017).

Antiretroviral therapy

While there is uncertainty over the timing of initiating antiretroviral therapy, some studies have suggested there may be benefits to beginning treatment early (When To Start Consortium et al., 2009; Cohen, 2011). Experimental studies also suggest that because ART reduces transmissibility, increasing coverage levels may reduce the prevalence of HIV (Cohen, 2011). However, drug-resistant strains can emerge, which can lead to treatment failure (Hué et al., 2009; Hamers et al., 2011). Immunoepidemiological models were used to understand these effects of ART, focusing on treatment timing (Sun et al., 2016; Yeghiazarian, Cumberland & Yang, 2013), coverage levels (Shen, Xiao & Rong, 2015), and drug resistance (Saenz & Bonhoeffer, 2013; Sun et al., 2016). The models showed that, in general, initiating treatment early (Yeghiazarian, Cumberland & Yang, 2013; Sun et al., 2016), increasing coverage (Shen, Xiao & Rong, 2015; Saenz & Bonhoeffer, 2013), and increasing effectiveness of ART (Shen, Xiao & Rong, 2015; Saenz & Bonhoeffer, 2013) reduces the prevalence of HIV.

However, in certain cases, increases in the prevalence of HIV may occur even with early treatment initiation, increased coverage, and increased effectiveness of ART to drug-sensitive strains. Models showed that as ART coverage levels increase, the prevalence of drug-resistant strains increase, which cause an increase in HIV prevalence (Saenz & Bonhoeffer, 2013). Prevalence can also increase if drug-resistant strains cause the drug efficacy to decrease significantly (Sun et al., 2016). These results imply that there may be an optimal therapy coverage level that will minimize the number of infections (Saenz & Bonhoeffer, 2013). Therefore, in these cases, the models suggest that HIV prevalence can be reduced by focusing efforts on decreasing the risk of drug resistance emergence (Saenz & Bonhoeffer, 2013).

Clinical studies have observed that under certain conditions, the prevalence of HIV increases when ART coverage levels increase (Zaidi et al., 2013). Zaidi et al. (2013) hypothesize that since ART reduces viral load, patients may live longer, and thus have the ability to infect more people. Immunoepidemiolgical models also observed this effect (Shen, Xiao & Rong, 2015), including a model of super-infection (Martcheva & Li, 2013). Both model outcomes are consistent with the hypothesis of Zaidi et al., since the models find that the increased prevalence is due solely to decreases in viral load (Shen, Xiao & Rong, 2015; Martcheva & Li, 2013). The model developed by Shen, Xiao & Rong (2015) found that this effect can be minimized if drug effectiveness is high.

Therapeutic interfering particles

Clinical trials have shown that therapeutic interfering particles (TIPs) have the potential to reduce within-host viral load (Levine et al., 2006) and transmit between hosts (Aaskov et al., 2006). Experimental studies have also shown that HIV transmission rates between hosts depend on the within-host viral load (Fraser et al., 2007). Based on these assumptions, an immunoepidemiological model is developed, which deploys TIPs to a small proportion (1%) of the population (Metzger, Lloyd-Smith & Weinberger, 2011). The effect on HIV prevalence due to deploying TIPs is compared to deploying ART and to deploying a hypothetical HIV vaccine. When TIPs have the ability to transmit between hosts, the model shows deploying TIPs reduces HIV prevalence to lower levels than deploying ART therapy or deploying vaccines. However, the model shows that if TIPs do not have the ability to transmit between hosts, then there is minimal effect on the reduction of HIV prevalence (Metzger, Lloyd-Smith & Weinberger, 2011). While more study of TIPs is needed, TIPs have the potential to be an effective therapy than either ART or vaccines.

HIV co-infection

Experimental studies suggest that co-infection may be responsible for increases seen in set-point viral load (spVL) at the within-host level over time (Modjarrad & Vermund, 2010). These increases due to co-infection vary substantially within-host (Kublin et al., 2005). Also, the concentrations of co-infection in high-risk groups versus low-risk groups may affect how HIV spreads in the general population (Abu-Raddad et al., 2008). To study the mechanisms responsible for these effects of co-infection, an immunoepidemiological model was developed (Cuadros & García-Ramos, 2012). They found that populations with higher spVL lead to higher increases in viral load due to co-infection, whereas populations with lower spVL leads to lower increases in viral load due to co-infection. This leads to a greater chance of co-infection increasing the prevalence of HIV in populations with high average spVL (Cuadros & García-Ramos, 2012). Therefore, the effects of co-infection may be mitigated by identifying the viral factors that can reduce the spVL in the population.