Complex dynamics of an epidemic model with saturated media coverage and recovery

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.

An Analytical Framework for Understanding Infection Progression Under Social Mitigation Measures

“…The model is a generalization of the compartmental SEIR model -socalled SPEIRD [57,58] -that accounts for the influence of social measures by mathematically representing them as an effect that removes susceptibles from the transmission process (and places them in a newly introduced Protected compartment). A similar approach to introduce the effects of distancing in compartmental models can be found in [32][33][34][35][36], and is in certain aspects advantageous over simply varying transmission coefficients in time, implemented in many models [4,8,22,[37][38][39]. SPEIRD also introduces additional compartments that directly correspond to epidemiological observables: the number of detected cases and the number of fatalities.…”

“…Progress has been made in various directions, e.g. by taking into account the effects of quarantine [1,2], temporary immunity [3], recurrent outbreaks [4], vaccination [5][6][7][8], different levels of population susceptibility [9], comorbidities [8,10], stratification by age [11][12][13], competitive virus strains of different severity and/or transmissibility [14,15], spatial diffusion [16], human mobility between different regions [17][18][19], availability of testing kits [20], hospital infrastructure [21] and media coverage [22,23] to name a few. In particular, the attempts to combat the disease led to the introduction of social distancing measures on the scales hardly imaginable before [24].…”

“…In particular, the attempts to combat the disease led to the introduction of social distancing measures on the scales hardly imaginable before [24]. While it is evident that they have a serious impact on the epidemiological dynamic, their effects are not yet well understood [25][26][27], despite a lot of undergoing effort to incorporate the influence of these measures into the existing epidemiological models [4,8,22,[28][29][30][31][32][33][34][35][36][37][38][39]. Common for all these extensions of epidemiological models (both those related to the effects of mitigation measures and to the inclusion of other relevant factors), is rely-…”

An analytical framework for understanding infection progression under social mitigation measures

“…Progress has been made in various directions, e.g. by taking into account the effects of quarantine [1,2], temporary immunity [3], recurrent outbreaks [4], vaccination [5][6][7][8], different levels of population susceptibility [9], comorbidities [8,10], stratification by age [11][12][13], competitive virus strains of different severity and/or transmissibility [14,15], spatial diffusion [16], human mobility between different regions [17][18][19], availability of testing kits [20], hospital infrastructure [21] and media coverage [22,23] to name a few. In particular, the attempts to combat the disease led to the introduction of social distancing measures on the scales hardly imaginable before [24].…”

“…In particular, the attempts to combat the disease led to the introduction of social distancing measures on the scales hardly imaginable before [24]. While it is evident that they have a serious impact on the epidemiological dynamic, their effects are not yet well understood [25][26][27], despite a lot of undergoing effort to incorporate the influence of these measures into the existing epidemiological models [4,8,22,[28][29][30][31][32][33][34][35][36][37][38][39]. Common for all these extensions of epidemiological models (both those related to the effects of mitigation measures and to the inclusion of other relevant factors), is rely-…”