Fig. 1
Classical SIR model scheme. The susceptible population becomes infected, which, in turn, becomes recovered. S = susceptible; I = infected; R = recovered
Fig. 2
Scheme of the SIRSI model considering genetics aspects of the vector. AA, Aa and aa mean dominant homozygotes, heterozygotes and recessive homozygotes, respectively, for the Susceptible (S) and Infected (I) mosquito populations. Sh, lh and Rh are the susceptible, infected and susceptible compartments for humans. Vectors become infected when they interact with an infected host; and susceptible humans become infected when they are bitten by an infected vector
Fig. 3
Results of simulation 1. a Susceptible (blue), infected (green) and recovered humans (red). b Infected aa (blue) and A_ (green) vectors. c Susceptible aa (blue) and A_ (green) vectors. d Susceptible (blue), infected (green) and total (red) populations of vectors disregarding the genetic separation. c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, θ = 6.353, βν = 0.4, K = 2 · 105, μaa = μAa = μΑΑ = 0.25, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents number of individuals. Image produced with MatLab®
Fig. 4
Results of simulation 1 (continued). a Allele frequencies of a (green) and A (blue). b Genotype frequencies of aa (blue), Aa (red) and AA (green). c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, θ = 6.353, βν = 0.4, K = 2 · 105, μaa = μAa = μΑΑ = 0.25, Sh = 9 · 103, lh = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, laa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, lv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents freqquency. Image produced with MatLab®
Fig. 5
Results of simulation 2. a Susceptible (blue), Infected (green) and recovered humans (red). b Infected aa (blue) and A_ (green) vectors. c Susceptible aa (blue) and A_ (green) vectors. d Susceptible (blue), infected (green) and total (red) populations of vectors disregarding the genetic separation. c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, θ = 6.353, βν = 0.4, K = 2 · 105, μaa = 0.01, μAa = βΑΑ = 0.25, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents number of individuals. Image produced with MatLab®
Fig. 6
Results of simulation 2 (continued). a Allele frequencies of a (green) and A (blue). b Genotype frequencies of aa (blue), Aa (red) and AA (green). c = 0.457 · 10−4, μh = 0.457 · 10−4, βΑ = 0.4, γ = 0.121, θ = 6.353, βv = 0.4, K = 2 · 105, μaa = 0.01, μAa = μAA = 0.25, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, Iaa = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents freqquency. Image produced with MatLab®
Fig. 7
Results of simulation 3. a Susceptible (blue), Infected (green) and recovered humans (red). b Infected aa (blue) and A_ (green) vectors. c Susceptible aa (blue) and A_ (green) vectors. d Susceptible (blue), infected (green) and total (red) populations of vectors disregarding the genetic separation. c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, γ = 6.353, βν = 0.4, K = 2 · 105, μaa = 0.25, μAa = μΑΑ = 0.01, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104.X axis represents time (days) and Y axis represents number of individuals. Image produced with MatLab®
Fig. 8
Results of simulation 3 (continued). a Allele frequencies of a (green) and A (blue). b Genotype frequencies of aa (blue), Aa (red) and AA (green), c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, θ = 6.353, βv = 0.4, K = 2 · 105, μaa = 0.25, μΑα = μAA = 0.01, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, lAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, Saa = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents freqquency. Image produced with MatLab®
Fig. 9
Simulation with the same conditions to first simulation, with time varying from 0 to 500. Legend: Susceptible (blue), infected (green) and recovered humans (red). c = 0.457 · 10−4, μh = 0.457 · 10−4, βh = 0.4, γ = 0.121, θ = 6.353, βν = 0.4, K = 2 · 105, μαα = μAa = μAA = 0.25, Sh = 9 · 103, Ih = 2 · 102, Rh = 3 · 102, Nh = 9.5 · 103, SAa = 2.375 · 103, IAa = 2.375 · 103, NAa = 4.75 · 103, Saa = 4.75 · 103, Iaa = 4.75 · 103, Naa = 9.5 · 103, SAA = 2.375 · 103, IAA = 2.375 · 103, NAA = 4.75 · 103, Iv = 3 · 104, Nv = 1.9 · 104. X axis represents time (days) and Y axis represents number of individuals. Image produced with MatLab®
Fig. 10
Smaller initial values. Simulations with the same conditions as the 1st, 2nd and 3rd simulations, but with initial values of variables ten times smaller than shown in
Table 2.
a complete charts of the simulation. The dashed square marks the region represented by the figure on the right.
b zoom on the left figure.
Dashed lines = susceptible humans;
continuous lines = infected humans;
blue lines = conditions similar to the first simulation;
yellow lines = conditions similar to the second simulation;
green lines = conditions similar to the third simulation. Graphics produced on Microsoft Excel
® with data obtained on MatLab
® simulations.
X axis represents time (days) and
Y axis represents number of individuals
Fig. 11
Total infected (continuous lines) and total susceptible (dashed lines) vectors In simulations 1, 2 and 3. Blue = First simulation;yellow = second simulation; green = third simulation. Graphics produced on Microsoft Excel®, but with data obtained on MatLab® simulations.X axis represents time (days) and Y axis represents number of individuals