Mathematical modelling and release thresholds of transgenic sterile mosquitoes

Figures & data

Table 1. Summary table of the results for models (2(2) $\begin{array}{r}\frac{\mathrm{d}S}{\mathrm{d}t}=\frac{aS}{S+c}(1-\xi \frac{aS}{S+c}S)S-\mu S.\end{array}$(2) ), (7(7) $\begin{array}{r}\frac{\mathrm{d}S}{\mathrm{d}t}=\frac{aS}{S+c}(1-\xi \frac{aS+2bc}{S+c}S)S-\mu S.\end{array}$(7) ), (19(19) $\begin{array}{rl}\frac{\mathrm{d}S}{\mathrm{d}t}& =\frac{aS}{S+c+\frac{\gamma bc}{S+c}S}(1-\xi \frac{aS+bc}{S+c}S)S-\mu S\\ & =\frac{aS}{(S+c{)}^2+\gamma bcS}(S+c-\xi (aS+bc)S)S-\mu S.\end{array}$(19) ), (29(29) $\begin{array}{rl}\frac{\mathrm{d}S}{\mathrm{d}t}& =\frac{aS}{S+c+\frac{\gamma bc}{S+c}S}(1-\xi \frac{aS+2bc}{S+c}S)S-\mu S\\ & =(\frac{aS((S-\xi (aS+bc))S+c)}{(S+c{)}^2+\gamma bcS}-\mu )S.\end{array}$(29) ).

	γ	Thresholds	c	Positive equilibria
EBS	0	$c_{EBS}=15973.0123$	15900	$S_{EBS}^{-}=49.5045$	$S_{EBS}^{+}=53.5369$
LBS	0	$c_{LBS}=68.0541$	65	$S_{LBS}^{-}=0.2311$	$S_{LBS}^{+}=0.3552$
EFK	0.4	$c_{EFK}=116.3435$	110	$S_{EFK}^{-}=0.4138$	$S_{EFK}^{+}=0.6641$
LFK	0.4	$c_{LFK}=6.8497$	6.5	$S_{LFK}^{-}=0.0156$	$S_{LFK}^{+}=0.5246$