Abstract
During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically and numerically investigate the dynamics of the proposed model. Given great difficulties caused by high nonlinearity in theoretical analysis, we separately considered subsystems with only nonlinear recovery or with only saturated media impact. For the model with only nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. Numerical simulations reveal the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, saddle-node bifurcation, homoclinic bifurcation and unstable limit cycle. So the limitation of medical resources induces rich dynamics and causes much difficulties in eliminating the infectious diseases. We then investigated the dynamics of the system with only saturated media impact and concluded that saturated media impact hardly induces the complicated dynamics. Further, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 2.86. Sensitivity analyses were carried out to quantify the relative importance of parameters in determining the cumulative number of infected individuals at the end of the first month of the outbreak. Combining with numerical analyses, we suggested that providing adequate medical resources and improving media response to infection or individuals’ response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.
Highlights
The emerging or re-emergent infectious diseases, including SARS(2003), HINI(2009) and COVID-19, have been threatening the public health and caused worrying concern amongst the public and health authorities
We suggested that providing adequate medical resources and improving media response to infection or individuals’ response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic
Some proposed the on-off media functions [5,6,7], where the media impact is triggered by the disease infection, they show that media coverage can be considered as an effective way to mitigate the disease spreading during the initial stage of an outbreak
Summary
The emerging or re-emergent infectious diseases, including SARS(2003), HINI(2009) and COVID-19, have been threatening the public health and caused worrying concern amongst the public and health authorities. To analyze the effect of medical conditions, Li and Zhang [16] proposed a SIR model in epidemic diseases using nonmonotone incidence and saturated recovery rates and investigated complex dynamics such as the saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation of codimension 2. It showed that a sufficient number of the beds is critical to control the epidemic. Our main purpose of this study is to propose a mathematical model with double nonlinear functions to investigate the impacts of saturated media coverage and limited medical resources on disease transmission and examine the rich dynamics induced by the nonlinearity.
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