Epidemic models with differential susceptibility and staged progression and their dynamics.
We formulate and study epidemic models with differential susceptibilities and staged-progressions, based on systems of ordinary differential equations, for disease transmission where the susceptibility of susceptible individuals vary and the infective individuals progress the disease gradually through stages with different infectiousness in each stage. We consider the contact rates to be proportional to the total population or constant such that the infection rates have a bilinear or standard form, respectively. We derive explicit formulas for the reproductive number R0, and show that the infection-free equilibrium is globally asymptotically stable if R0>1 when the infection rate has a bilinear form. We investigate existence of the endemic equilibrium for the two cases and show that there exists a unique endemic equilibrium for the bilinear incidence, and at least one endemic equilibrium for the standard incidence when R0>1.
Hyman
James M
JM
Theoretical Division, MS-B284, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, United States. hyman@lanl.gov
Li
Jia
J
D001699:Biometry / Q000379:methods*; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D018450:Disease Progression; D004198:Disease Susceptibility / Q000453:epidemiology*; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D015995:Prevalence