Dynamics of competition model between two plants based on stoichiometry.

The dynamics of two-plant competitive models have been widely studied, while the effect of chemical heterogeneity on competitive plants is rarely explored. In this study, a model that explicitly incorporates light and total phosphorus in the system is formulated to characterize the impacts of limited carbon and phosphorus on the dynamics of the two-plant competition system. The dissipativity, existence and stability of boundary equilibria and coexistence equilibrium are proved, when the two plants compete for light equally. Our simulations indicate that, with equal competition for light ($ b_{12} = b_{21} $) and a fixed total phosphorus in the system ($ T $), plants can coexist with moderate light intensity ($ K $). A higher $ K $ tends to favor the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). When $ K $ is held constant, a moderate level of $ T $ leads to the dominance of the plant with a lower phosphorus loss rate ($ d_1 $ vs $ d_2 $). At high $ T $ levels, both plants can coexist. Moreover, our numerical analysis also shows that, when the competition for light is not equal, the low level of total phosphorus in the system may lead the model to be unstable and have more types of bistability compared with the two-dimensional Lotka-Volterra competition model.

Recursive Zero-COVID model and quantitation of control efforts of the Omicron epidemic in Jilin province.

Since the beginning of March 2022, the epidemic due to the Omicron variant has developed rapidly in Jilin Province. To figure out the key controlling factors and validate the model to show the success of the Zero-COVID policy in the province, we constructed a Recursive Zero-COVID Model quantifying the strength of the control measures, and defined the control reproduction number as an index for describing the intensity of interventions. Parameter estimation and sensitivity analysis were employed to estimate and validate the impact of changes in the strength of different measures on the intensity of public health preventions qualitatively and quantitatively. The recursive Zero-COVID model predicted that the dates of elimination of cases at the community level of Changchun and Jilin Cities to be on April 8 and April 17, respectively, which are consistent with the real situation. Our results showed that the strict implementation of control measures and adherence of the public are crucial for controlling the epidemic. It is also essential to strengthen the control intensity even at the final stage to avoid the rebound of the epidemic. In addition, the control reproduction number we defined in the paper is a novel index to measure the intensity of the prevention and control measures of public health.

Modeling and Evaluation of the Joint Prevention and Control Mechanism for Curbing COVID-19 in Wuhan.

The spread of COVID-19 in Wuhan was successfully curbed under the strategy of "Joint Prevention and Control Mechanism." To understand how this measure stopped the epidemics in Wuhan, we establish a compartmental model with time-varying parameters over different stages. In the early stage of the epidemic, due to resource limitations, the number of daily reported cases may lower than the actual number. We employ a dynamic-based approach to calibrate the accumulated clinically diagnosed data with a sudden jump on February 12 and 13. The model simulation shows reasonably good match with the adjusted data which allows the prediction of the cumulative confirmed cases. Numerical results reveal that the "Joint Prevention and Control Mechanism" played a significant role on the containment of COVID-19. The spread of COVID-19 cannot be inhibited if any of the measures was not effectively implemented. Our analysis also illustrates that the Fangcang Shelter Hospitals are very helpful when the beds in the designated hospitals are insufficient. Comprised with Fangcang Shelter Hospitals, the designated hospitals can contain the transmission of COVID-19 more effectively. Our findings suggest that the combined multiple measures are essential to curb an ongoing epidemic if the prevention and control measures can be fully implemented.

Modeling the outbreak and control of African swine fever virus in large-scale pig farms.

African swine fever virus (ASFV) leads to a highly contagious, lethal and economically devastating disease among pigs. Since no effective treatment for the disease, it is crucial to investigate its transmission mechanism and control strategies in large-scale pig farms. We first established a toy model to explore ASFV spread in one pig unit. Then a switching patch model was developed to capture its spread from one initial epidemic pig house consecutively to others, even the whole farm. Assessing innocent culling rates of three large-scale epidemic pig farms in Jiangsu Province showed that it is unnecessary to slaughter all pigs in the farms compulsively. Then we explored how the disinfection and fixation of employees impact ASFV spread in the farms. To control ASFV, we can block or slow down its spreading by improving the efficiency of disinfection and decreasing employee population to some extend. We can also shrink potential areas to be infected by properly improving the matching refinement degree among employees and houses. Some essential requirements for large-scale pig farms are presented to reduce their ASFV spreading risk, which can be helpful for animal health authorities in establishing regulation to standardize large-scale pig farms.

Dynamic modeling and optimal control of cystic echinococcosis.

BACKGROUND: Cystic echinococcosis is one of the most severe helminth zoonosis with a drastic impact on human health and livestock industry. Investigating optimal control strategy and assessing the crucial factors are essential for developing countermeasures to mitigate this disease. METHODS: Two compartment models were formulated to study the dynamics of cystic echinococcosis transmission, to evaluate the effectiveness of various control measures, and to find the optimal control strategy. Sensitive analyses were conducted by obtaining PRCCs and contour plot was used to evaluate the effect of key parameters on the basic reproduction number. Based on forward-backward sweep method, numerical simulations were employed to investigate effects of key factors on the transmission of cystic echinococcosis and to obtain the optimal control strategy. RESULTS: The food resources of stray dog and invalid sheep vaccination rate, which are always neglected, were significant to the transmission and control of cystic echinococcosis. Numerical simulations suggest that, the implementation of optimal control strategy can significantly reduce the infections. Improving the cost of health education and domestic dog deworming could not decrease human infections. CONCLUSIONS: Our study showed that only a long-term use of the optimal control measures can eliminate the disease. Meanwhile, during the intervention, sheep vaccination and stray dogs disposing should be emphasized ahead of domestic dogs deworming to minimize the control cost. Simultaneously reducing other wild intermediate hosts and strengthening the sheep vaccination as well as disposing the stray dogs would be most effective.

Stoichiometric Modeling of Aboveground-Belowground Interaction of Herbaceous Plant and Two Herbivores.

In a grassland ecosystem, the dynamics and coexistence mechanisms of two herbivores competing for one herbaceous plant have been widely studied, while the chemical heterogeneity of herbaceous plant's aboveground and belowground parts is usually ignored in dynamic modeling. Based on the traditional two herbivore-one herbaceous plant competition model, a new stoichiometric competition model, which incorporates the chemical heterogeneity of herbaceous plants, is formulated to investigate effects of the aboveground-belowground interactions and the chemical heterogeneity on the dynamics of the two herbivore-one herbaceous plant system. We perform theoretical analysis for the stability of boundary equilibria and show that a stable coexistent equilibrium is possible with two herbivores on one herbaceous plant. Moreover, numerical simulations reveal that various light intensity and nitrogen input can also allow all populations to coexist in periodic oscillations or irregularly cyclic oscillations. Our findings further indicate that when the nitrogen input is fixed, higher light intensity leads to a dominance of the lower N-demand herbivore, while the light intensity is fixed, higher nitrogen input leads to a dominance of the higher N-demand herbivore. Moderate levels of light and nutrient could promote the coexistence of two herbivores and herbaceous plant. This study also explains the functional mechanism for the decline of species diversity in response to nitrogen enrichment.

Impact of disposing stray dogs on risk assessment and control of Echinococcosis in Inner Mongolia.

Echinococcosis has been recognized as one of the most important helminth zoonosis in China. Available models always consider dogs as the mainly definitive hosts. However, such models ignore the distinctions between domestic dogs and stray dogs. In this study, we propose a 10-dimensional dynamic model distinguishing stray dogs from domestic dogs to explore the special role of stray dogs and potential effects of disposing stray dogs on the transmission of Echinococcosis. The basic reproduction number R0, which measures the impact of both domestic dogs and stray dogs on the transmission, is determined to characterize the transmission dynamics. Global dynamic analysis of the model reveals that, without disposing the stray dogs, the Echinococcosis becomes endemic even the domestic dogs are controlled. Moreover, due to the difficulties in estimating the parameters involved in R0 with real data and the limitation of R0 in real-world applications, a new risk assessment tool called relative risk index Irisk is defined for the control of zoonotic diseases, and the studies of the risk assessment for Echinococcosis infection show that it is essential to distinguish stray dogs from domestic dogs in applications.

Stoichiometric modeling of aboveground-belowground interaction of herbaceous plant.

Grassland ecosystems are the most widely distributed terrestrial ecosystems of the world. Many studies focus on aboveground grassland, but the belowground grassland is less explored because of the difficulty of sampling. Furthermore, the above-and-below ground biomass allocation mechanism of herbs is still disputed between the isometric growth hypothesis and the optimal partitioning hypothesis. In this study, a regrowth dynamic model, based on nutrient dynamics and stoichiometry, is proposed and analyzed to investigate the interaction between the aboveground and belowground herbaceous plants. The global dynamics of the belowground and aboveground biomass is well analyzed. Numerical simulations conclude that the herbaceous plant's biomass allocation mechanism for the aboveground and the belowground is in conformity with optimal partitioning at the beginning of growth, when the environment changes, it conforms to the constraints of isometric growth. Moreover, the dynamics of the model agree well with experimental data, which reveals that the model can express the relationship between aboveground and belowground biomass. Finally, a regrowth-herbivore model is established to explore the effects of nutrition and light intensity on the dynamics of plant and herbivore biomass.