Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system

Abstract

Motivated by the failure of current methods to control dengue fever, we formulate a mathematical model to assess the impact on the spread of a mosquito-borne viral disease of a strategy that releases adult male insects homozygous for a dominant, repressible, lethal genetic trait. A dynamic model for the female adult mosquito population, which incorporates the competition for female mating between released mosquitoes and wild mosquitoes, density-dependent competition during the larval stage, and realization of the lethal trait either before or after the larval stage, is embedded into a susceptible-exposed-infectious-susceptible human-vector epidemic model for the spread of the disease. For the special case in which the number of released mosquitoes is maintained in a fixed proportion to the number of adult female mosquitoes at each point in time, we derive mathematical formulas for the disease eradication condition and the approximate number of released mosquitoes necessary for eradication. Numerical results using data for dengue fever suggest that the proportional policy outperforms a release policy in which the released mosquito population is held constant, and that eradication in approximately 1 year is feasible for affected human populations on the order of 10(5) to 10(6), although the logistical considerations are daunting. We also construct a policy that achieves an exponential decay in the female mosquito population; this policy releases approximately the same number of mosquitoes as the proportional policy but achieves eradication nearly twice as fast.

Fig. 1.

The RIDL eradication threshold (θ*) for the proportional policy vs. the logarithm of the pretreatment mosquito-to-human population ratio (N_V(0)/N_H), which is generated by varying the population parameter K, for late-lethal (—), early-lethal (- -), and the asymptotic {as N_V(0)/N_H → ∞} limit (· · ·).

Fig. 2.

The number of RIDL mosquitoes required for eradication in Eq. 8 vs. the number of days until eradication t* [i.e., I_V(t*) ≤ 0.1] for both late-lethal (—) and early-lethal (- -) for all three policies: the proportional policy (red), the constant policy (green), and the trajectory policy (black). These curves are generated by varying the free parameter (θ, C, and φ, respectively) in the three policies (the curves are in the upper-left portion of the graphs for larger values of the free parameters) and numerically computing Eqs. 1–5 with the initial state variables set at their nontrivial pretreatment steady-state values (see SI Appendix, Section 1). We consider four values of N_V(0)/N_H. (a) 4, (b) 8, (c) 12, and (d) 16.