infectious immigrants at stage $i$
        $a$                                 Biting rate
      $\mu_h$                        Host’s natural death rate
   $\beta_{v,h}$           Host’s infectiousness by mosquitoes per biting
    $\beta_{i}$       Vector’s infectiousness by host at stage $i$ per biting
      $\nu_h$      Host’s rate at which the exposed individuals become infectious
     $\eta_i$        Per capita recovery rate of an infected host at stage $i$
   $\gamma_{ij}$      Host’s per capita progression rate from stage $i$ to $j$
   $\delta_{ij}$      Host’s per capita regression rate from stage $i$ to $j$
      $\mu_v$                     Vectors’ natural mortality rate
    $\delta_v$                Vectors’ control-induced mortality rate
      $\nu_v$           Rate at which the exposed vectors become infectious

  : Description of the parameters used in System (\[ModelAD\]).[]{data-label="tab:Param"}

Model (\[ModelAD2Compact\]) follows an $SEI^nR-SEI$ structure. That is, of the host and vector populations dynamics follow an and $SEI^nR$ and $SEI$ types of model, respectively. The choices are make to capture some key features in modeling different vector-borne diseases. Indeed, many special cases could be obtained from our general framework to fit a particular arboviral disease. For instance, if $\nu_h\to\infty$, the Host’s dynamics will be an $SI^nR$ model. An $SIR-SI$ model have been considered for malaria [@tumwiine2010host] and Dengue [@Esteva98Dengue] while an $SI^nR-SI$ model was deemed more suited for tick-borne relapsing fever [@johnson2016modeling; @palmer2018dynamics].\
Model (\[ModelAD2Compact\]) generalizes other 