R0 and sensitivity analysis of a predator-prey model with seasonality and maturation delay

Spatial heterogeneity analysis for the transmission of syphilis disease in China via a data-validated reaction-diffusion model

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.

Partial tipping in bistable ecological systems under periodic environmental variability

Periodic environmental variability is a common source affecting ecosystems and regulating their dynamics. This paper investigates the effects of periodic variation in species growth rate on the population dynamics of three bistable ecological systems. The first is a one-dimensional insect population model with coexisting outbreak and refuge equilibrium states, the second one describes two-species predator-prey interactions with extinction and coexistence states, and the third one is a three-species food chain model where chaotic and limit cycle states may coexist. We demonstrate with numerical simulations that a periodic variation in species growth rate may cause switching between two coexisting attractors without crossing any bifurcation point. Such a switchover occurs only for a specific initial population density close to the basin boundary, leading to partial tipping if the frozen system is non-chaotic. Partial tipping may also occur for some initial points far from the basin boundary if the frozen system is chaotic. Interestingly, the probability of tipping shows a frequency response with a maximum for a specific frequency of periodic forcing, as noticed for equilibrium and non-equilibrium limit cycle systems. The findings suggest that unexpected outbreaks or abrupt declines in population density may occur due to time-dependent variations in species growth parameters. Depending on the selective frequency of the periodic environmental variation, this may lead to species extinction or help the species to survive.

Threshold dynamics of a reaction-advection-diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction-advection-diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number R 0 and show that the disease-free periodic solution is globally attractive whenR 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case whenR 0 > 1 . Moreover, we find that R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment

With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.

Effectiveness of phase synchronization in chaotic food chain model with refugia and Allee effects during seasonal fluctuations

Seasonal effects powerfully shape the population dynamics with periodic climate changes because species naturally adjust their dynamics with seasonal variations. In response to these effects, sometimes population dynamics exhibit synchrony or generate chaos. However, synchronized dynamics enhance species' persistence in naturally unstable environments; thus, it is imperative to identify parameters that alter the dynamics of an ecosystem and bring it into synchrony. This study examines how ecological parameters enable species to adapt their dynamics to seasonal changes and achieve phase synchrony within ecosystems. For this, we incorporate seasonal effects as a periodic sinusoidal function into a tri-trophic food chain system where two crucial bio-controlling parameters, Allee and refugia effects, are already present. First, it is shown that the seasonal effects disrupt the limit cycle and bring chaos to the system. Further, we perform rigorous mathematical analysis to perform the dynamical and analytical properties of the nonautonomous version of the system. These properties include sensitive dependence on initial condition (SDIC), sensitivity analysis, bifurcation results, the positivity and boundedness of the solution, permanence, ultimate boundedness, and extinction scenarios of species. The SDIC characterizes the presence of chaotic oscillations in the system. Sensitivity analysis determines the parameters that significantly affect the outcome of numerical simulations. The bifurcation study concerning seasonal parameters shows a higher dependency of species on the frequency of seasonal changes than the severity of the season. The bifurcation study also examines the bio-controlling parameters and reveals various dynamic states within the system, such as fold, transcritical branch points, and Hopf points. Moreover, the mathematical analysis of our seasonally perturbed system reveals the periodic coexistence of all species and a globally attractive solution under certain parametric constraints. Finally, we examine the role of essential parameters that contribute to phase synchrony. For this, we numerically investigate the defining role of the coupling dimension coefficient, bio-controlling parameters, and other parameters associated with seasonality. This study infers that species can tune their dynamics to seasonal effects with low seasonal frequency, whereas the species' tolerance for the severity of seasonal effects is relatively high. The research also sheds light on the correlation between the degree of phase synchrony, prey biomass levels, and the severity of seasonal forcing. This study offers valuable insights into the dynamics of ecosystems affected by seasonal perturbations, with implications for conservation and management strategies.

Basic reproduction ratio of a mosquito-borne disease in heterogeneous environment

To explore the influence of spatial heterogeneity on mosquito-borne diseases, we formulate a reaction-diffusion model with general incidence rates. The basic reproduction ratio [Formula: see text] for this model is introduced and the threshold dynamics in terms of [Formula: see text] are obtained. In the case where the model is spatially homogeneous, the global asymptotic stability of the endemic equilibrium is proved when [Formula: see text]. Under appropriate conditions, we establish the asymptotic profiles of [Formula: see text] in the case of small or large diffusion rates, and investigate the monotonicity of [Formula: see text] with respect to the heterogeneous diffusion coefficients. Numerically, the proposed model is applied to study the dengue fever transmission. Via performing simulations on the impacts of certain factors on [Formula: see text] and disease dynamics, we find some novel and interesting phenomena which can provide valuable information for the targeted implementation of disease control measures.

Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.