Table 1.
Variables and parameters in model (1).
Fig 1.
Numerical solutions of the endemic equilibria Meq as a function of R0 with different k values, fixing z = 0.96.
Fig 2.
Transmission dynamics of model (3) and (4) considering no application of MDA and one round of MDA at time t = 1 with k = 0.05 and R0 = 2.
(a) M0 < M*. (b) M* < M0 < M*. (c) M0 = M*. (d) M0 > M*.
Fig 3.
Transmission dynamics of model (3) and (4) by considering the implementation of biannual and annual MDA, M0 > M*, varying ϵ and choosing z = 0.96, R0 = 2 and ω = 0.5.
Top row: biannual MDA. Bottom row: annual MDA. Left column: k = 0.05. Right column: k = 0.5.
Fig 4.
The comparison of the overestimate (5) and (6) and original model (3) and (4) by considering the implementation of biannual MDA with ϵ = 0.4 and ω = 0.5 and varying k and R0 values.
(a) R0 = 2, k = 0.05, n > 5.83 and MSE = 0.1258 × 10−4. (b) R0 = 2, k = 0.5, n > 8.34 and MSE = 0.2167 × 10−2. (c) R0 = 1.8, k = 0.05, n > 2.86 and MSE = 0.5217 × 10−6. (d) R0 = 1.8, k = 0.5, n > 5.38 and MSE = 0.6392 × 10−3.
Fig 5.
The comparison of solutions (5) and (6) and numerical solutions of model (3) and (4) by considering the implementation of annual MDA with ϵ = 0.4 and ω = 0.5 and varying k and R0 values.
(a) R0 = 2, k = 0.05, n > 7.29 and MSE = 0.6333 × 10−4. (b) R0 = 2, k = 0.5, n > 13.14 and MSE = 0.0156. (c) R0 = 1.8, k = 0.05, n > 2.96 and MSE = 0.2106 × 10−5. (d) R0 = 1.8, k = 0.5, n > 6.29 and MSE = 0.2264 × 10−2.
Fig 6.
The comparison of models (3) and (9) when no control strategy has been applied.
Both models have the same outcomes for arbitrary initial points, R0 = 2 and k = 0.05. (a) M0 > M* and . (b) M* < M0 < M* and
. (c) M0 < M* and
.
Fig 7.
The transmission dynamics of model (9) and (10) for a range of , ϵ and ω values, with k = 0.05 and R0 = 2.
(a) ω = ϵ = 0.6 and . (b) ω = ϵ = 0.6 and
. (c)
around the neighbourhood of
.
Fig 8.
Numerical comparison of model (12) and (13) and model (9) and (10) by considering the implementation of biannual MDA with ϵ = ω = 0.6 and varying k and R0 values.
(a) k = 0.05, R0 = 1.8 and MSE for Mnt and Mt are 5.9377 × 10−5 and 1.1881 × 10−5, respectively. (b) k = 0.2, R0 = 1.8 and MSE for Mnt and Mt are 1.5909 × 10−3 and 2.2534 × 10−4, respectively. (c) k = 0.05, R0 = 2 and MSE for Mnt and Mt are 2.6274 × 10−4 and 2.9925 × 10−5, respectively. (d) k = 0.2, R0 = 2 and MSE for Mnt and Mt are 4.5018 × 10−3 and 4.7219 × 10−4, respectively.
Fig 9.
Numerical comparison of model (12) and (13) and model (9) and (10) for annual MDA with ϵ = ω = 0.6 and varying k and R0 values.
(a) k = 0.05, R0 = 1.8 and MSE for Mnt and Mt are 1.4241 × 10−4 and 4.9371 × 10−5, respectively. (b) k = 0.2, R0 = 1.8 and MSE for Mnt and Mt are 3.2954 × 10−3 and 9.5671 × 10−4, respectively. (c) k = 0.05, R0 = 2 and MSE for Mnt and Mt are 4.3739 × 10−4 and 1.1943 × 10−4, respectively. (d) k = 0.2, R0 = 2 and MSE for Mnt and Mt are 8.6585 × 10−3 and 2.1309 × 10−3, respectively.
Fig 10.
Numerical results of model (3) and (4) and model (9) and (10) by varying ϵ and applying the coverage of MDA data from the TUMIKIA community-based biannual deworming control strategy.
(a) Disease persistence if ϵ < 0.44. (b) Disease extinction is possible if ϵ ≥ 0.61. (c) Disease extinction is possible for model (3) and (4) if ϵ ≥ 0.44, but the disease will remain in endemic state for model (9) and (10) if ϵ < 0.61.
Fig 11.
The numerical results of model (3) and (4) and model (9) and (10) by varying ϵ and applying the coverage of MDA data from the TUMIKIA community-based annual deworming control strategy.
(a) Disease persistence if ϵ < 0.73. (b) Disease extinction if ϵ ≥ 0.85. (c) Disease elimination is possible for model (3) and (4) if ϵ ≥ 0.73, but the disease will remain in endemic state for model (9) and (10) if ϵ < 0.85.
Fig 12.
Numerical solutions of model (9) and (10) with an additional round of TUMIKIA community-based biannual deworming strategy.
Fig 13.
Numerical solutions of model (9) and (10) with an additional round of TUMIKIA community-based annual deworming strategy.