## 5 Numerical Examples
### Parameter Adjustment  
Replication cycles of the cassava virus are studied in [38; 39]. Viruses themselves do not have a \"life cycle\", as they require a host to replicate. In the whitefly life cycle, the adulthood spans from their second to fourth week, leading to multiple generations per year. The baseline life cycle though is that of the cassava plant: the virus can persist in an infected plant for its entire life span, which is typically 1-3 years, depending on the variety and cultivation practices. The literature tells us that, after planting, the cassava harvest cycle is between the fourth and ninth month [40]. So, as a mean, a reference period of 200 days is chosen.  
To give some orientation of the numerical parameters, we compare the parameters of our model in Equations (13)-(17) with the parameters in some studies in the literature, namely, those of Bahity-Maranya (2022) (2022) (2022) (model 2),  
\[\frac{dS_{c}}{dt} =r_{c}\bigg{(}1-\frac{N_{c}}{\kappa_{c}}\bigg{)}S_{c}+\phi I_{c}-aS _{c}I_{w}-\psi S_{c} \tag{65}\] \[\frac{dE_{c}}{dt} =r_{c}\bigg{(}1-\frac{N_{c}}{\kappa_{c}}\bigg{)}\rho E_{c}+aS_{c} I_{w}-(\psi+\epsilon)E_{c}\] (66) \[\frac{dI_{c}}{dt} =\epsilon E_{c}-(\psi+\phi)I_{c}\] (67) \[\frac{dS_{w}}{dt} =\bigg{(}1-\frac{N_{w}}{\kappa_{w}}\bigg{)}r_{w}N_{w}-(b(E_{c}+I_ {c})+cI_{h})S_{w}-\omega S_{w}\] (68) \[\frac{dI_{w}}{dt} =(b(E_{c}+I_{c})+cI_{h})S_{w}-\omega I_{w}\] (69) \[\frac{dS_{h}}{dt} =r_{h}\bigg{(}1-\frac{N_{h}}{\kappa_{h}}\bigg{)}S_{h}-dS_{h}I_{w }-\eta S_{h}\] (70) \[\frac{dI_{h}}{dt} =dS_{h}I_{w}-\eta I_{h} \tag{71}\]  
and [PERSON] et al. (2019) (2022) (model 3),  
\[\frac{dS_{r}}{dt} =r_{1}S_{r}\bigg{(}1-\frac{S_{r}}{k_{1}}\bigg{)}-\beta_{1}S_{r}I_{ V}-\rho_{1}S_{r} \tag{72}\] \[\frac{dS_{C}}{dt} =r_{2}S_{C}\bigg{(}1-\frac{S_{C}}{k_{2}}\bigg{)}-\beta_{2}S_{C}I_{ V}-\rho_{2}S_{C}\] (73) \[\frac{dI_{C}}{dt} =\beta_{2}S_{C}I_{V}+\beta_{1}S_{r}I_{V}-\rho_{3}I_{C}-aI_{C}\] (74) \[\frac{dS_{V}}{dt} =b(S_{V}+I_{V})\bigg{(}1-\frac{S_{V}+I_{V}}{k_{3}}\bigg{)}-\beta_{ 3}S_{V}I_{C}-\gamma S_{V}\] (75) \[\frac{dI_{V}}{dt} =\beta_{3}S_{V}I_{C}-\gamma I_{V} \tag{76}\]  
The parameters of these models are compared in the concordance in Table 2, where corresponding parameters are placed in the same row.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Model 1** & & **Model 2 [202]** & & **Model 3 [202]** \\  & **(System (13)–(17))** & & **(System (65)–(71))** & & **(System (72)–(76) )** \\ \hline \(b(t)\) & 0.05 day\({}^{-1}\) & \(r_{c}\) & 0.05 day\({}^{-1}\) & \(r_{1}\) & 0.025 day\({}^{-1}\) \\  & & & 0.2 day\({}^{-1}\) & \(r_{2}\) & 0.2 day\({}^{-1}\) \\ \hline \(\theta\) & 1.0 plant/m\({}^{2}\) & \(\kappa_{c}\) & 0.7 m\({}^{-2}\) & \(k_{1}\) & 3000 \\  & & & \(k_{2}\) & 2000 \\ \hline \(\beta(t)\) & 0.001 vector\({}^{-1}\) day\({}^{-1}\) & \(a\) & 0.008 plant\({}^{-1}\) day\({}^{-1}\) & \(\beta_{1}\) & 0.0012 vector\({}^{-1}\) day\({}^{-1}\) \\  & & & & \(\beta_{2}\) & 0.003 vector\({}^{-1}\) day\({}^{-1}\) \\ \hline \(h(t)\) & 0.03 day\({}^{-1}\) & \(\psi\) & 0.003 day\({}^{-1}\) & \(\rho_{1}\) & 0.005 day\({}^{-1}\) \\  & & & & \(\rho_{2}\) & 0.003 day\({}^{-1}\) \\ \hline \(g(t)\) & 0 day\({}^{-1}\) & & & & \\ \hline \(a(t)\) & 0.1 day\({}^{-1}\) & \(r_{h}\) & 0.02 plant\({}^{-1}\) day\({}^{-1}\) & \(b\) & 0.5 vector\({}^{-1}\) day\({}^{-1}\) \\ \hline \(\gamma(t)\) & 0.01 plant\({}^{-1}\) day\({}^{-1}\) & \(d\) & 0.008 day\({}^{-1}\) & \(\beta_{3}\) & 0.002 plant\({}^{-1}\) day\({}^{-1}\) \\ \hline \(\mu\) & 0.02 day\({}^{-1}\) & \(\eta\) & 0.001 day\({}^{-1}\) & \(\gamma\) & 0.0782 day\({}^{-1}\) \\ \hline \(\alpha\) & - & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Concordance table comparing parameters of three models.