ODE boxes without parameters. All dotted lines and boxes can be turned on or off through parameter value choices.

Diseases currently supported

  1. None : Choosing “None” for disease gives full user control over the model (picture above, ODE and parameters written out below)
  2. Dengue : Base of 4 host and 3 mosquito boxes, but can allow exposed classes of host and mosquito if desired (not allowed right now, but something I can change)
  3. Chikungunya: Similar to Dengue, base of 4 and 3 boxes assumed, but can allow for exposed classes.
  4. Malaria : Base of all 5 host and 4 mosquito boxes. Also allows very slow waning of immunity.
  5. Zika : Not yet, but soon

Full ODE equations

\(\frac{dS_h}{dt} = \mu_hN_h - (B(N_h, T)\beta_{mh}(T)\frac{I_m}{N_h} + \mu_h)S_h + \delta_hR_h\)

\(\frac{dE_h}{dt} = B(N_h, T)\beta_{mh}(T)\frac{I_m}{N_h}S_h[\omega_{Eh}] - (\mu_h + \gamma_h)E_h\)

\(\frac{dI_h}{dt} = B(N_h, T)\beta_{mh}(T)\frac{I_m}{N_h}S_h[1 - \omega_{Eh}][1 - \omega_{Ah}] + \gamma_hE_h[1 - \omega_{Ah}] - (\eta_h + \alpha_h + \mu_h)I_h\)

\(\frac{dI_{Ah}}{dt} = B(N_h, T)\beta_{mh}(T)\frac{I_m}{N_h}S_h[1 - \omega_{Eh}][\omega_{Ah}] + \gamma_hE_h[\omega_{Ah}] - (\eta_h + \mu_h)I_Ah\)

\(\frac{dR_h}{dt} = \eta_h(I_h + I_{Ah}) - (\mu_h + \delta_h)R_h\)

\(\frac{dA_m}{dt} = \phi(T)(1 - \frac{A_m}{k(N_h)})(S_m + I_m) - (\eta_A(T) + \mu_A(T))A_m\)

\(\frac{dS_m}{dt} = \eta_A(T)A_m - (B(N_h, T)\beta_{hm}(\frac{I_h}{N_h} + \frac{I_{Ah}}{N_h}\psi_h) + \mu_m(T))S_m\)

\(\frac{dE_m}{dt} = B(N_h, T)\beta_{hm}(\frac{I_h}{N_h} + \frac{I_{Ah}}{N_h}\psi_h)[\omega_{Em}]S_m - \gamma_mE_m - \mu_m(T)E_m\)

\(\frac{dI_m}{dt} = B(N_h, T)\beta_{hm}(\frac{I_h}{N_h} + \frac{I_{Ah}}{N_h}\psi_h)[1 - \omega_{Em}]S_m + \gamma_mE_m - \mu_m(T)I_m\)

State variables and parameters

State variables:

\(\frac{dS_h}{dt}\) : Susceptible hosts
\(\frac{dE_h}{dt}\) : Exposed hosts
\(\frac{dI_h}{dt}\) : Infected hosts
\(\frac{dI_{Ah}}{dt}\): Infected but asymptomatic hosts
\(\frac{dR_h}{dt}\) : Recovered hosts
\(\frac{dA_m}{dt}\) : Aquatic mosquitoes (eggs + larvae + pupae)
\(\frac{dS_m}{dt}\) : Susceptible adult mosquitoes
\(\frac{dE_m}{dt}\) : Exposed adult mosquitoes
\(\frac{dI_m}{dt}\) : Infectious adult mosquitoes

Parameters:

\(\mu_h\) : Mortality rate of humans
\(B\) : Average daily biting rate of adult mosquiotes
\(\beta_{mh}\) : Transmission probability from mosquito to host per bite
\(\eta_{h}\) : Rate of exit from a viremic state for humans (recovery)
\(\phi\) : Number of eggs produced by each mosquitoe per day
\(k\) : Number of larvae per human
\(\eta_a\) : Maturation rate from aquatic stage mosquitoes to adult
\(\mu_a\) : Natural mortality of aquatic stage mosquitoes
\(\beta_{hm}\) : Transmission probability from host to mosquito per bite
\(\mu_m\) : Average mortality rate of mosquitoes
\(\gamma_h\) : Host rate of leaving latent period
\(\gamma_m\) : Mosquito rate of leaving latent period
\(\delta_h\) : Host waning immunity rate
\(\alpha_h\) : Parasite induced host mortality rate
\(\omega_{Eh}\) : Proportion of new host infections that first move to the exposed category. For simplicity, for now just choose 1 or 0.
\(\omega_{Em}\) : Proportion of new mosquito infections that first move to the exposed category. For simplicity, for now just choose 1 or 0.
\(\omega_{Ah}\) : Proportion of host infections asymptomatic
\(\psi_h\) : Asymptomatic infection modifier to host to mosquito transmission probability

Assumptions based on user choices

  1. Defining a specific disease selects parameter values for disease-specific parameters based on (what is now as of Oct 8) a pretty narrow lit search
  2. Choosing a mosquito or disease when temperature dependence is turned on will select parameters that have happened to be measured for your choice
    2.1) All other parameter values for the temperature dependence will be average across species based on your choice of temperate or tropical