Meili Li

Political instability often exhibits long-term oscillatory patterns, commonly referred to in Structural-Demographic Theory as secular cycles. Although existing computational approaches, such as the Multi-Path Forecasting framework, can reproduce historical instability trends through high-dimensional simulations, they often lack the analytical tractability needed to clarify the structural mechanisms underlying these oscillations. To address this limitation, we propose a reduced-dimensional continuous-time model consisting of three coupled ordinary differential equations that capture the nonlinear feedback among radicalization, collective violence, and accumulated structural pressure. Using a mean-field approximation for the population reservoir, we derive a minimal dynamical system that preserves the essential structure of the original framework. Stability analysis based on the Routh–Hurwitz criterion shows that equilibrium stability is governed by the rate of exogenous economic decline. We further establish the occurrence of a supercritical Hopf bifurcation, whereby sufficiently severe economic deterioration destabilizes the equilibrium and gives rise to a stable limit cycle representing persistent secular cycles of political violence. Numerical simulations support the analytical results and provide a rigorous mathematical foundation for the endogenous periodicity of social unrest.

Original antigenic sin (OAS) describes the phenomenon in which prior exposure to an antigen weakens the adaptive antibody response to a subsequent heterologous infection. This phenomenon can diminish the effectiveness of immunity acquired through vaccination or previous infections. We demonstrate that OAS arises because CD4+ T cell proliferation and regulation signals are antigen‐nonspecific. Rapidly responding memory CD4+ T cells trigger regulatory T cell (Tregs) responses, which prematurely suppress the naïve CD4+ T cell response, leading to a similar OAS effect in CD4+ T cells. This mechanism is illustrated through a mathematical model incorporating naïve and memory CD4+ T cell proliferation, interleukin‐2 (IL‐2), and Tregs. The model, calibrated with experimental data, employs numerical simulations to analyse how CD4+ T cell responses vary with the degree of cross‐reactivity between memory CD4+ T cells and the antigen associated with the secondary infection. The findings indicate that the immune response is weakest at an intermediate level of cross‐reactivity, a key characteristic of OAS. This mechanism may also explain OAS in antibody responses.

The perceived infection risk changes individual behaviors, which further affects the disease dynamics. This perception is influenced by social communication, including surveying their social network neighbors about the fraction of infected neighbors and averaging their neighbors’ perception of the risk. We model the interaction of disease dynamics and risk perception on a two-layer random network that combines a social network layer with a contact network layer. We found that if information spreads much faster than disease, then all individuals converge on the true prevalence of the disease. On the other hand, if the two dynamics have comparable speeds, the risk perception still converges to a value uniformly on the network. However, the perception lags behind the true prevalence and has a lower peak value. We also study the behavior change caused by the perception of infection risk. This behavior change may affect the disease dynamics by reducing the transmission rate along the edges of the contact network or by breaking edges and isolating the infectious individuals. The effects on the basic reproduction number, the peak size, and the final size are studied. We found that these two effects give the same basic reproduction number. We find edge-breaking has a larger effect on reducing the final size, while reducing the transmission rate has a larger effect on reducing the peak size, which is true for both scale-free and Poisson networks.

Background: In March 2022, the Omicron variant of SARS-CoV-2 spread rapidly in Shanghai, China. The city adopted strict non-pharmacological intervention (NPI) measures, including lockdown (implemented on March 28 in Pudong and April 1 in Puxi) and blanket PCR testing (April 4). This study aims to understand the effect of these measures.Methods: We tabulated daily case counts from official reports and fitted a two-patch stochastic SEIR model to the data for the period of March 19 to April 21. This model considered two regions in Shanghai, namely Pudong and Puxi, as the implementation of control measures in Shanghai was carried out on different dates in these regions. We verified our fitting results using the data from April 22 to June 26. Finally, we applied the point estimate of parameter values to simulate our model while varying the dates of control measure implementation, and studied the effectiveness of the control measures.Results: Our point estimate for the parameter values yields expected case counts that agree well the data for both the periods from March 19 to April 21 and from April 22 to June 26. Lockdown did not significantly reduce the intra-region transmission rates. Only about 21% cases were reported. The underlying basic reproduction numberR₀was 1.7, and the control reproduction number with both lockdown and blanket PCR testing was 1.3. If both measures were implemented on March 19, only about 5.9% infections would be prevented.Conclusions: Through our analysis, we found that NPI measures implemented in Shanghai were not sufficient to reduce the reproduction number to below unity. Thus, earlier intervention only has limited effect on reducing cases. The outbreak dies out because of only 27% of the population were active in disease transmission, possibly due to a combination of vaccination and lockdown.

We propose a new method to estimate the change of the effective reproduction number with time, due to either disease control measures or seasonally varying transmission rate. We validate our method using a simulated epidemic curve and show that our method can effectively estimate both sudden changes and gradual changes in the reproduction number. We apply our method to the COVID-19 case counts in British Columbia, Canada in 2020, and we show that strengthening control measures had a significant effect on the reproduction number, while relaxations in May (business reopening) and September (school reopening) had significantly increased the reproduction number from around 1 to around 1.7 at its peak value. Our method can be applied to other infectious diseases, such as pandemics and seasonal influenza.

In this paper, we used a generic two-stage population model to derive an adaptive dynamical system for the evolution of reproduction age and studied how this evolution is driven by the harvest of adults. We considered the tradeoffs between maturation rate and fecundity, juvenile mortality, and adult mortality. We analyzed the benefit and cost of faster maturation under each tradeoff that drives the evolution. We found that harvesting adults affects the evolution of maturation by affecting the benefit. For the tradeoff between maturation and juvenile mortality, harvesting adults does not affect the benefit and thus, does not affect optimal maturation strategy. For the other two tradeoffs, harvesting adults affects the benefit through the equilibrium adult/juvenile ratio, which is determined by the density dependence of juveniles. Harvesting adults causes a slower maturation only if it significantly reduces this ratio, which can only happen with very strong adult protection to juveniles. Otherwise, harvesting adults always causes a faster maturation.

The COVID-19 outbreak has been a serious public health threat worldwide. We use individually documented case descriptions of COVID-19 from China (excluding Hubei Province) to estimate the distributions of the generation time, incubation period, and periods from symptom onset to isolation and to diagnosis. The recommended 14-day quarantine period may lead to a 6.7% failure for quarantine. We recommend a 22-day quarantine period. The mean generation time is 3.3 days and the mean incubation period is 7.2 days. It took 3.7 days to isolate and 6.6 days to diagnose a patient after his/her symptom onset. Patients may become infectious on average 3.9 days before showing major symptoms. This makes contact tracing and quarantine ineffective. The basic reproduction number is estimated to be 1.54 with contact tracing, quarantine and isolation, mostly driven by super spreaders.

In this paper, we propose sex-structured mathematical models in terms of continuous-time differential equations. We investigate the interactive dynamics of the sex-structured wild and sterile mosquitoes from several aspects including the existence of equilibria and their stability. We consider different strategies of releasing the sterile mosquitoes to control mosquitoes in an effective way. In addition, numerical simulations are provided to illustrate the dynamical features of the models.

In this paper we study a kind of second-order impulsive stochastic differential equations with state-dependent delay in a real separable Hilbert space. Some sufficient conditions for the approximate controllability of this system are formulated and proved under the assumption that the corresponding deterministic linear system is approximately controllable. The results concerning the existence and approximate controllability of mild solutions have been addressed by using strongly continuous cosine families of operators and the contraction mapping principle. At last, an example is given to illustrate the theory.

The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.