Linking Spontaneous Behavioral Changes to Disease Transmission Dynamics: Behavior Change Includes Periodic Oscillation.

Behavior change significantly influences the transmission of diseases during outbreaks. To incorporate spontaneous preventive measures, we propose a model that integrates behavior change with disease transmission. The model represents behavior change through an imitation process, wherein players exclusively adopt the behavior associated with higher payoff. We find that relying solely on spontaneous behavior change is insufficient for eradicating the disease. The dynamics of behavior change are contingent on the basic reproduction number R a corresponding to the scenario where all players adopt non-pharmaceutical interventions (NPIs). When R a < 1 , partial adherence to NPIs remains consistently feasible. We can ensure that the disease stays at a low level or maintains minor fluctuations around a lower value by increasing sensitivity to perceived infection. In cases where oscillations occur, a further reduction in the maximum prevalence of infection over a cycle can be achieved by increasing the rate of behavior change. When R a > 1 , almost all players consistently adopt NPIs if they are highly sensitive to perceived infection. Further consideration of saturated recovery leads to saddle-node homoclinic and Bogdanov-Takens bifurcations, emphasizing the adverse impact of limited medical resources on controlling the scale of infection. Finally, we parameterize our model with COVID-19 data and Tokyo subway ridership, enabling us to illustrate the disease spread co-evolving with behavior change dynamics. We further demonstrate that an increase in sensitivity to perceived infection can accelerate the peak time and reduce the peak size of infection prevalence in the initial wave.

Lessons drawn from Shanghai for controlling highly transmissible SARS-CoV-2 variants: insights from a modelling study.

BACKGROUND: The continuous emergence of novel SARS-CoV-2 variants with markedly increased transmissibility presents major challenges to the zero-COVID policy in China. It is critical to adjust aspects of the policy about non-pharmaceutical interventions (NPIs) by searching for and implementing more effective ways. We use a mathematical model to mimic the epidemic pattern of the Omicron variant in Shanghai to quantitatively show the control challenges and investigate the feasibility of different control patterns in avoiding other epidemic waves. METHODS: We initially construct a dynamic model with a core step-by-step release strategy to reveal its role in controlling the spread of COVID-19, including the city-based pattern and the district-based pattern. We used the least squares method and real reported case data to fit the model for Shanghai and its 16 districts, respectively. Optimal control theory was utilized to explore the quantitative and optimal solutions of the time-varying control strength (i.e., contact rate) to suppress the highly transmissible SARS-CoV-2 variants. RESULTS: The necessary period for reaching the zero-COVID goal can be nearly 4 months, and the final epidemic size was 629,625 (95%CI: [608,049, 651,201]). By adopting the city-based pattern, 7 out of 16 strategies released the NPIs more or earlier than the baseline and ensured a zero-resurgence risk at the average cost of 10 to 129 more cases in June. By adopting the district-based pattern, a regional linked release can allow resumption of social activity to ~ 100% in the boundary-region group about 14 days earlier and allow people to flow between different districts without causing infection resurgence. Optimal solutions of the contact rate were obtained with various testing intensities, and higher diagnosis rate correlated with higher optimal contact rate while the number of daily reported cases remained almost unchanged. CONCLUSIONS: Shanghai could have been bolder and more flexible in unleashing social activity than they did. The boundary-region group should be relaxed earlier and more attention should be paid to the centre-region group. With a more intensive testing strategy, people could return to normal life as much as possible but still ensure the epidemic was maintained at a relatively low level.

Optimal strategies for coordinating infection control and socio-economic activities.

It becomes challenging to identify feasible control strategies for simultaneously relaxing the countermeasures and containing the Covid-19 pandemic, given China's huge population size, high susceptibility, persist vaccination waning, and relatively weak strength of health systems. We propose a novel mathematical model with waning of immunity and solve the optimal control problem, in order to provide an insight on how much detecting and social distancing are required to coordinate socio-economic activities and epidemic control. We obtain the optimal intensity of countermeasures, i.e., the dynamic nucleic acid screening and social distancing, under which the health system is functioning normally and people can engage in a certain level of socio-economic activities. We find that it is the isolation capacity or the restriction of the case fatality rate (CFR) rather than the hospital capacity that mainly determines the optimal strategies. And the solved optimal controls under quarterly CFR restrictions exhibit oscillations. It is worth noticing that, if without considering booster or very low booster rate, the optimal strategy is a "on-off" mode, alternating between lock down and opening with certain social distancing, which reflects the importance and necessity of China's static management on a certain area during Covid-19 outbreak. The findings suggest some feasible paths to smoothly transit from the Covid-19 pandemic to an endemic phase.

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

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.

Linking the disease transmission to information dissemination dynamics: An insight from a multi-scale model study.

During the outbreak of emerging infectious diseases, information dissemination dynamics significantly affects the individuals' psychological and behavioral changes, and consequently influences on the disease transmission. To investigate the interaction of disease transmission and information dissemination dynamics, we proposed a multi-scale model which explicitly models both the disease transmission with saturated recovery rate and information transmission to evaluate the effect of information transmission on dynamic behaviors. Considering time variation between information dissemination, epidemiological and demographic processes, we obtained a slow-fast system by reasonably introducing a sufficiently small quantity. We carefully examined the dynamics of proposed system, including existence and stability of possible equilibria and existence of backward bifurcation, by using the fast-slow theory and directly investigating the full system. We then compared the dynamics of the proposed system and the essential thresholds based on two methods, and obtained the similarity between the basic dynamical behaviors of the slow system and that of the full system. Finally, 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 3.25. Numerical analysis suggested that information transmission about COVID-19 pandemic caused by media coverage can reduce the peak size, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.