Fig 1.
Modules in the MGDrivE 2 framework.
(A) Genetic inheritance is embodied by a three-dimensional tensor referred to as an “inheritance cube.” Maternal and paternal genotypes are depicted on the x and y-axes and offspring genotypes on the z-axis. (B) Mosquito life history is modeled according to an egg-larva-pupa-adult (female and male) life cycle in which density dependence occurs at the larval stage, and life cycle parameters may vary as a function of environmental variables over time. Genotypes are tracked across all life stages, and females obtain a composite genotype upon mating—their own and that of the male they mate with. Egg genotypes are determined by the inheritance cube. (C) The landscape represents a metapopulation in which mosquitoes are distributed across population nodes and move between them according to a dispersal kernel. Population sizes and movement rates may vary as a function of environmental variables. (D) The epidemiology module describes reciprocal transmission of a vector-borne pathogen between mosquitoes and humans. This requires modeling human as well as mosquito populations, and the number of individuals having each infectious state. Epidemiological parameters may vary as a function of environmental variables.
Fig 2.
MGDrivE 2 includes two basic models for reciprocal pathogen transmission between mosquitoes and humans—one for malaria (A), and one for arboviruses (B). In both cases, female mosquitoes emerge from pupae at a rate equal to dP/2 as susceptible adults (SV), become exposed/latently infected (EV,1) at a rate equal to the force of infection in mosquitoes, λV, and progress to infectiousness (IV) through the extrinsic incubation period (EIP = 1/γV), which is divided into n bins to give an Erlang-distributed dwell time. The mortality rate, μF, is the same for female mosquitoes in each of these states. For malaria (A), susceptible humans (SH) become infected/infectious (IH) at a rate equal to the force of infection in humans, λH, and recover at rate r, becoming susceptible again. For arboviruses (B), susceptible humans (SH) become exposed/latently infected (EH) at a rate equal to λH, progress to infectiousness (IH) at rate equal to γH, and recover (RH) at rate, r. Infection dynamics couple the mosquito and human systems via the force of infection terms; λV is a function of IH, and λH is a function of IV, shown via red edges.
Fig 3.
Stochastic Petri net (SPN) implementation of MGDrivE 2.
(A) Petri net representation of the life history module. The set of purple circles corresponds to places, P, and red rectangles to transitions, T. This Petri net shows a model in which development times for the egg stage are Erlang-distributed with shape parameter n = 2, and for the larval stage are Erlang-distributed with shape parameter n = 3. Population dynamics are derived directly from this graph. E.g. The transition corresponding to oviposition has one edge beginning at F, meaning at least one female mosquito must be present for oviposition to occur. When oviposition occurs, a token is added to E1 (new eggs are laid) and a token is returned to F. (B) Conceptual representation of the SPN software architecture showing the separation between the model representation (blue circles) and set of sampling algorithms (red rectangles). These two components of the codebase meet at the simulation API, enabling users to match models and simulation algorithms interchangeably. Output may be returned as an array in R for exploratory work, or written to CSV files for large simulations.
Fig 4.
Example MGDrivE 2 simulations for a split gene drive system designed to drive a malaria-refractory gene in a confinable and reversible manner into an An. gambiae s.l. mosquito population with seasonal population dynamics and transmission intensity calibrated to a setting resembling the island of Grand Comore, Union of the Comoros.
The split drive system resembles one recently engineered in Ae. aegypti [2]–the only split drive system in a mosquito vector to date. In the modeled system, two components–the Cas9 and guide RNA (gRNA)–are present at separate, unlinked loci, and a disease-refractory gene is linked to the gRNA. Four alleles are considered at the gRNA locus: an intact gRNA/refractory allele (denoted by “H”), a wild-type allele (denoted by “W”), a functional, cost-free resistant allele (denoted by “R”), and a non-functional or otherwise costly resistant allele (denoted by “B”). At the Cas9 locus, two alleles are considered: an intact Cas9 allele (denoted by “C”), and a wild-type allele (denoted by “W”). Model parameters describing the construct, mosquito bionomics and malaria transmission are summarized in S1 Table. (A) Climatological time-series data—temperature in red and rainfall in blue—that were used to calculate time-varying adult mosquito mortality rate and larval carrying capacity, respectively. The resulting adult female population size is shown in green. (B) Allele frequencies for adult female mosquitoes over the simulation period. Grey vertical bars beginning at year three denote eight consecutive weekly releases of 50,000 male mosquitoes homozygous for both the gRNA and Cas9 alleles (H and C, respectively). (C) Spread of the malaria-refractory trait through the female mosquito population, and consequences for mosquito and human infection status. Following releases of the drive system at year three, the proportion of refractory female mosquitoes (solid red line) increases and the proportion of infectious mosquitoes (dotted light blue line) declines. As humans recover from infection and less develop new infections, the P. falciparum parasite rate (solid green line) declines until it reaches near undetectable levels by year five. (D) Human malaria incidence is halted by the beginning of year four.