This is my first time using the StackExchange and I was hoping someone could help me find the Jacobian Matrix for the ODEs I am working with. I am working with three populations; Humans, Ticks, and Carriers. The ODEs involving exposed and infected compartments are:
EH/dt = (βHH * IH) + (βCH * IC) + (βTH * IT) - (deltaH + muH)EH IH/dt = (deltaH * EH) - (alpha + gamma + muH) * IH) ET/dt = (piT * βTTV * IT) + (βCT * IC) + (BTTH * IT) - (deltaT + muT) * ET IT/dt = (deltaT * ET) - (muT * IT) EC/dt = (βTC * IT) - (deltaC + muC) * EC IC/dt = (deltaC * EC) - (muC * IC)
Where alpha represents the human recovery rate, gamma represents the human death rate from the disease, piT represents the tick birth rate, mu represents the natural death rate respectively, and delta represents the incubation period respectively for humans, ticks, and carriers. Please let me know if there is any clarification needed or any further information that would be useful such as my full model or code. Thank you very much.