A Generalized Discrete Dynamic Model for Human Epidemics

Wenjun Zhang; Zeliang Chen; Yi Lu; Zhongmin Guo; Yanhong Qi; Guoling Wang; Jiahai Lu

So far a lot of dynamic models have been developed and used in the mechanic analysis and prediction of animal epidemics. Among them the differential equations based models are the mainstream methods, including SIR model (Kermack and McKendrick, 1927) , Anderson-May model (Anderson and May, 1981) , the models of Zhang et al. (1997 , 2011 ), etc. Zhang et al. (1997 model was a group of differential-integral equations mainly treating susceptible and infected insect populations. The improved model (Zhang et al., 2011) was composed of nearly twenty differential equations supplemented by other equations. In these models, both susceptible and infected populations were treated as population density, and susceptible population interacts with infected population mainly through feeding on virus on the leaves spread by insects that died from virus infection. Serving as both explanatory and simulation models, they have demonstrated the better performance. Both SIR model (Kermack and McKendrick, 1927) and Anderson-May model (Anderson and May, 1981) include differential equations (correspondingly, difference equations) for susceptible (s) and infected (i) populations rather than population density, and the two populations interact with each other through the interaction term, ps(t)i(t) (Fuxa and Tanada, 1987) . Nevertheless, numerous simulation results showed that both of their models are extremely sensitive to some of the key parameters and initial population sizes, especially the infection coefficient, p. Given true parameters and initial conditions, it was so difficult to synchronously obtain realistic results for population size and key time points (such as the peak time) although both of them are better explanatory models for the epidemic dynamics. Furthermore, the important parameters such as incubation period, hospitalization term, etc., were not included in such explanatory models and most of the other models (Chen et al., 2020a) . In present paper we developed a generalized discrete dynamic model for human epidemics, and sensitivity analysis and scenario prediction was made, aiming to provide a novel simulation tool for future uses.