Mathematical Biosciences最新文献

In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is more costly (financial or health-related costs) for higher ages. This work considers an age-structured population transmission model with imperfect vaccination. We aim to compare the social and individual costs of vaccination, assuming that disease costs are age-dependent, while the disease’s dynamic is age-independent. A model for pathogen deterministic dynamics in a population consisting of juveniles and adults, assumed to be rational agents, is introduced. The parameter region for which vaccination has a positive social impact is fully characterized and the Nash equilibrium of the vaccination game is obtained. Finally, collective strategies designed to promote voluntary vaccination, without compromising social welfare, are discussed.

We present a model for the dynamics of two interacting pathogen variants in a wild animal host population. Using the next-generation matrix approach we define the invasion threshold for one pathogen variant when the other is already established and at steady state. We then provide explicit criteria for the special cases where: i) the two pathogen variants exclude each other; ii) one variant excludes the other; iii) the population dynamics of hosts infected with both variants are independent of the order of infection; iv) there is no interaction between the variants; and v) one variant enhances transmission of the other.

COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible–Exposed–Infectious–Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model’s ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models.

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction–diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction–diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction–diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.

Non-pharmaceutical personal protective (NPP) measures such as face masks use, and hand and respiratory hygiene can be effective measures for mitigating the spread of aerosol/airborne diseases, such as COVID-19, in the absence of vaccination or treatment. However, the usage of such measures is constrained by their inherent perceived cost and effectiveness for reducing transmission risk. To understand the complex interaction of disease dynamics and individuals decision whether to adopt NPP or not, we incorporate evolutionary game theory into an epidemic model such as COVID-19. To compare how self-interested NPP use differs from social optimum, we also investigated optional control from a central planner’s perspective. We use Pontryagin’s maximum principle to identify the population-level NPP uptake that minimizes disease incidence by incurring the minimum costs. The evolutionary behavior model shows that NPP uptake increases at lower perceived costs of NPP, higher transmission risk, shorter duration of NPP use, higher effectiveness of NPP, and shorter duration of disease-induced immunity. Though social optimum NPP usage is generally more effective in reducing disease incidence than self-interested usage, our analysis identifies conditions under which both strategies get closer. Our model provides new insights for public health in mitigating a disease outbreak through NPP.

Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise.

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when $R_0=1$. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

Based on the distinctive spatial diffusion characteristics observed in syphilis transmission patterns, this paper introduces a novel reaction–diffusion model for syphilis disease dynamics, incorporating general incidence functions within a heterogeneous environment. We derive the basic reproduction number essential for threshold dynamics and investigate the uniform persistence of the model. We validate the model and estimate its parameters by employing the multi-objective Markov Chain Monte Carlo (MCMC) method, using real syphilis data from the years 2004 to 2018 in China. Furthermore, we explore the impact of spatial heterogeneity and intervention measures on syphilis transmission. Our findings reveal several key insights: (1) In addition to the original high-incidence areas of syphilis, Xinjiang, Guizhou, Hunan and Northeast China have also emerged as high-incidence regions for syphilis in China. (2) The latent syphilis cases represent the highest proportion of newly reported cases, highlighting the critical importance of considering their role in transmission dynamics to avoid underestimation of syphilis outbreaks. (3) Neglecting spatial heterogeneity results in an underestimation of disease prevalence and the number of syphilis-infected individuals, undermining effective disease prevention and control strategies. (4) The initial conditions have minimal impact on the long-term spatial distribution of syphilis-infected individuals in scenarios of varying diffusion rates. This study underscores the significance of spatial dynamics and intervention measures in assessing and managing syphilis transmission, which offers insights for public health policymakers.

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter $R_{\ast }>1$, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for $R_{\ast }<1$, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of $R_{\ast }$ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. $R_{\ast }$ describes the strength of the transmission to infectious classes other than the $I$-(acute) type infections. The epidemic outbreak conditions and the structure of $R_{\ast }$ appearing in this model are both responsible for the existence of endemic states.

Ventricular ventricular interaction (VVI) affects blood volume and pressure in the right and left ventricles of the heart due to the location and balance of forces on the septal wall separating the ventricles. In healthy patients, the pressure of the left ventricle is considerably higher than the right, resulting in a septal wall that bows into the right ventricle. However, in patients with pulmonary hypertension, the pressure in the right ventricle increases significantly to a point where the pressure is similar to or surpasses that of the left ventricle during portions of the cardiac cycle. For these patients, the septal wall deviates towards the left ventricle, impacting its function. It is possible to study this effect using mathematical modeling, but existing models are nonlinear, leading to a system of algebraic differential equations that can be challenging to solve in patient-specific optimizations of clinical data. This study demonstrates that a simplified linearized model is sufficient to account for the effect of VVI and that, as expected, the impact is significantly more pronounced in patients with pulmonary hypertension.