Modeling the dynamics of Plasmodium vivax infection and hypnozoite reactivation in vivo

Abstract

The dynamics of Plasmodium vivax infection is characterized by reactivation of hypnozoites at varying time intervals. The relative contribution of new P. vivax infection and reactivation of dormant liver stage hypnozoites to initiation of blood stage infection is unclear. In this study, we investigate the contribution of new inoculations of P. vivax sporozoites to primary infection versus reactivation of hypnozoites by modeling the dynamics of P. vivax infection in Thailand in patients receiving treatment for either blood stage infection alone (chloroquine), or the blood and liver stages of infection (chloroquine + primaquine). In addition, we also analysed rates of infection in a study in Papua New Guinea (PNG) where patients were treated with either artesunate, or artesunate + primaquine. Our results show that up to 96% of the P. vivax infection is due to hypnozoite reactivation in individuals living in endemic areas in Thailand. Similar analysis revealed the around 70% of infections in the PNG cohort were due to hypnozoite reactivation. We show how the age of the cohort, primaquine drug failure, and seasonality may affect estimates of the ratio of primary P. vivax infection to hypnozoite reactivation. Modeling of P. vivax primary infection and hypnozoite reactivation provides important insights into infection dynamics, and suggests that 90-96% of blood stage infections arise from hypnozoite reactivation. Major differences in infection kinetics between Thailand and PNG suggest the likelihood of drug failure in PNG.

Fig 1. Schematic of primaquine treated P.vivax infection in the study population.

(A) shows the effect of successful liver and blood stage treatment of individuals in a P.vivax endemic region over time. Individuals become infected due to primary infection at the rate k, as the hypnozoite reservoir has been successfully cleared. In panel B, individuals are treated for blood stage parasites only. This results in blood stage infection from hypnozoite reactivation at the rate kc, and new infectious mosquito bites at the rate k. Panel C shows a scenario where hypnozoites and blood stage parasites are successfully cleared in some proportion of the population (top half of panel), and this population experiences new primary infections only (at rate k). The remaining proportion of the population has primaquine resistance, and thus retains their reservoir of hypnozoites. These resistant individuals will become infected at the rate k for primary infection and kc for hypnozoite reactivation.

Fig 2. Schematic of P. vivax infection.

The dynamics of P. vivax infection starts from a successful mosquito inoculation. We denote the rate of successful mosquito inoculation as M. Each successful mosquito inoculation successfully infects on average S liver cells (ie: leads to S blood stage infections). A fraction f of infected liver cells proceeds to early infection, leaving a fraction (1-f) as hypnozoites to later reactivate. The rate of new blood stage infections is thus MS, which is equivalent to rate of initiation of new infection observed in individuals treated with either chloroquine plus primaquine, or artesunate plus primaquine (k in Equations 1–4). Hypnozoites (H) are formed at a rate (1-f)MS and reactivate at rate aH. The total rate of blood stage infection (from new infection plus hypnozoites) settles to MS (ie: the rate of blood stage infection is the same as the rate of successful infection of new liver cells in steady state). The total rate of new blood stage infection MS is equivalent to the infection rate observed in individuals treated with chloroquine or artesunate alone ((k(1+c)) in Equations 1–4).

Fig 3. The rate of primary infection versus hypnozoite reactivation in Thailand.

(A) Modelling was performed to estimate the rate of blood stage infection in individuals treated with chloroquine (blue), or chloroquine + Primaquine (black). The actual rate of inoculation of new infections cannot be directly estimated from this data. Panels B-D show several possible rates if infectious inoculation (green dashed line) that could explain the data. (B), The minimal rate of inoculation occurs if every new inoculation were observed as a primary infection. In this case, the infectious inoculation rate equals the rate of infection in the CQ+PQ group (a new inoculation every 588 days), and each inoculation must lay down 24 hypnozoites that later reactivate. (C), The maximal rate of infectious inoculation would be if each inoculation lead to either one primary infection, or one later reactivation. In this case, only 4% of inoculations would present as primary infections, and the rest lay down one hypnozoites that later reactivates. (D), The most likely infectious inoculation rate appears an intermediate between these extremes (of (B) and (C)), in which only a portion of inoculations leads to primary infection, and each inoculation lays down several hypnozoites. In panel D the green line illustrates a rate at infectious inoculation where ≈20% of inoculations leads to primary infection, and each inoculation lays down ≈5 hypnozoites.

Fig 4. Primaquine therapy in PNG.

Fitting of the mathematical model to data from PNG. (A) The models fit (solid lines) assuming 100% efficacy of primaquine treatment over the first 60 days after treatment is shown at left. The black line indicates the fit for the AS+PQ group, and the blue line for the AS only group. (B) The best fit model for the full 280 day time course is shown at right, assuming that primaquine is ineffective in a proportion of individuals (B).

Fig 5. Dynamics of P. vivax infection with time.

(A) Modeling the proportion of infections from new primary infection versus hypnozoite reactivation with time. In the presence of a constant rate of inoculation, the rate of primary infection (black line) will rapidly reach equilibrium and be constant with time. However, the rate of hypnozoite reactivation (blue line) will take some time to reach its steady state level. The time taken to reach this is dependent on the rate of reactivation of hypnozoites (a _H). (B) shows best-fits of time to Pv infection in children < 5 years or subjects >5 years old in the Thai study.

Fig 6. Impact of seasonality in transmission.

(A–C) The rate of primary infection over time (black line) and hypnozoite reactivation with time (coloured lines) with seasonal transmission is plotted for different rates of hypnozoite reactivation. Rapid hypnozoite reactivation (half-life of one month) leads to rapid fluctuation in the rate of infection from hypnozoite reactivation. Slower rates of reactivation, equivalent of a half-life of six months (B) or 12 months (C) lead to more stable levels of hypnozoite reactivation. (D), The effect of seasonality on the ratio of hypnozoite reactivation versus primary infection when reactivation is of order of a month (red line), order of six months (green line) and order of a year (blue line). The ratio of infections from hypnozoite reactivation versus primary infection is paradoxically more stable in the setting of rapid hypnozoite reactivation (red line).