Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics

In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if R 0 < 1 , and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point R 0 = 1 and the local stability of endemic equilibrium if R 0 > 1 . Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.

Spatial demography

Demographic methods can be used to study the spatial response of individuals and populations to current global changes. The first mechanism underlying range shifts is a change in the spatial distribution of births and deaths. The spatial regression of demographic rates with geostatistical and spatially explicit models documents the intrinsic growth rate across the range of a population. The population distribution is expected to shift towards areas with the largest intrinsic growth rate, both mechanistically and because these areas are attractive to dispersing individuals. The second mechanism is indeed movement, including emigration away from places that recently became inhospitable and immigration into newly available locations. The analysis of dispersal fluxes using movement data, or indirectly by comparing the observed and intrinsic growth rates in integrated population models, documents these fluxes. Combining these two mechanisms in integral projection models or in individual-based simulations is expected to yield major advances in predictive spatial ecology, that is, mechanistic species distribution models.

Stability of May’s Host–Parasitoid model with variable stocking upon parasitoids

Using the Kolmogorov–Arnold–Mozer (KAM) theory, we investigate the stability of May’s host–parasitoid model’s solutions with proportional stocking upon the parasitoid population. We show the existence of the extinction, boundary, and interior equilibrium points. When the host population’s intrinsic growth rate and the releasement coefficient are less than one, both populations are extinct. There are an infinite number of boundary equilibrium points, which are nonhyperbolic and stable. Under certain conditions, there appear 1:1 nonisolated resonance fixed points for which we thoroughly described dynamics. Regarding the interior equilibrium point, we use the KAM theory to prove its stability. We give a biological meaning of obtained results. Using the software package Mathematica, we produce numerical simulations to support our findings.

The dynamics of evolutionary rescue from a novel pathogen threat in a host metapopulation

When a novel disease strikes a naïve host population, there is evidence that the most immediate response can involve host evolution while the pathogen remains relatively unchanged. When hosts also live in metapopulations, there may be critical differences in the dynamics that emerge from the synergy among evolutionary, ecological, and epidemiological factors. Here we used a Susceptible-Infected-Recovery model to explore how spatial and temporal ecological factors may drive the epidemiological and rapid-evolutionary dynamics of host metapopulations. For simplicity, we assumed two host genotypes: wild type, which has a positive intrinsic growth rate in the absence of disease, and robust type, which is less likely to catch the infection given exposure but has a lower intrinsic growth rate in the absence of infection. We found that the robust-type host would be strongly selected for in the presence of disease when transmission differences between the two types is large. The growth rate of the wild type had dual but opposite effects on host composition: a smaller increase in wild-type growth increased wild-type competition and lead to periodical disease outbreaks over the first generations after pathogen introduction, while larger growth increased disease by providing more susceptibles, which increased robust host density but decreased periodical outbreaks. Increased migration had a similar impact as the increased differential susceptibility, both of which led to an increase in robust hosts and a decrease in periodical outbreaks. Our study provided a comprehensive understanding of the combined effects among migration, disease epidemiology, and host demography on host evolution with an unchanging pathogen. The findings have important implications for wildlife conservation and zoonotic disease control.

Differential effects on the toxicity and bioconcentration of hexavalent and trivalent chromium on the rotifer Lecane papuana (Rotifera: Monogononta)

Heavy metals are still a matter of concern as they might reach aquatic environments due to anthropogenic activities like metal-mechanic or mining, which are part of the main economic activities in different regions around the world. The exposure to chromium may be linked to discharges from automotive and tannery industries, representing a threat to aquatic biota. In the environment, chromium presents two stable forms, the trivalent (CrIII) and the hexavalent (CrVI), which differ on their chemical properties, and thus, on their bioavailability and effects on organisms exposed to this metal. Therefore, this work was aimed to assess the effects of both chromium III and VI on the demographic responses of the rotifer Lecane papuana and describe how the bioconcentration of chromium affects survival and fecundity. For this purpose, acute toxicity (48 h) and chronic toxicity test (alterations on the intrinsic growth rate) were carried out. Moreover, the bioconcentration factor (BCF) and metal body burden (MBB) were estimated after 24-h exposure to either CrIII or CrVI. Our results indicate that CrIII was less toxic according to their respective LC50 values (CrIII = 2.613 mg/L; CrVI = 0.177 mg/L). The intrinsic growth rate was significantly affected by CrIII while CrVI caused no significant changes but only at 0.0885 mg/L, which represents 0.5 of their respective LC50 value. Bioconcentration experiments demonstrated that L. papuana accumulated more CrIII before causing deleterious effects, although it was not as toxic as CrVI, which elicited toxic effects on L. papuana at concentrations of environmental concern.

On the Random Non-Autonomous Logistic Equation with Time-Dependent Coefficients

In this paper, we deal with the non-autonomous logistic growth model with time-dependent intrinsic growth rate and carrying capacity. Accounting for errors in recorded data, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty of the model output is quantified by approximations of the first probability density function via the random variable transformation method. A numerical example illustrates the results.

Characteristic and evaluation of sustainability artisanal bonito (Auxis spp.) fisheries in the Prigi Bay and surrounding waters

Bonito plays an important role as the main ingredient for marinated products and provides a livelihood for coastal communities. Given the emergence of Indonesia's over-exploited small-scale marine fisheries resources, this study aims to characterize and evaluate fishery’s sustainability based on bioeconomic analyses. Time series catch and effort data were collected from 2005 to 2019 provided by Archipelagic Fishing Port of Prigi. Five surplus production models were also employed to generate catch-and-effort-based biological parameters, namely intrinsic growth rate (r), catchability (q), and carrying capacity (K). By adding economy parameters such as cost and price, the sustainability of catch and effort was also estimated at three management conditions. The catch abundance was peaked in April and September, characterized by the lack of rain. The CPUE was varied inter-annually. However, it declined during the last decade, indicating that the stock size was decreased. Although the average catches from 2015-2019 (9,984 tons) are lower than CMSY (11,695 tons). However, the effort in 2019 (15,239 trips) has exceeded EMEY (14,237 trips). Hence, reducing fishing efforts or maintaining it at E2018 level was suggested as a precaution to keep the fishery’s sustainability and simultaneously generate optimum profit.

Period-Doubling and Neimark–Sacker Bifurcations of a Beddington Host-Parasitoid Model with a Host Refuge Effect

In this paper, we explore the dynamics of a certain class of Beddington host-parasitoid models, where in each generation a constant portion of hosts is safe from attack by parasitoids, and the Ricker equation governs the host population. Using the intrinsic growth rate of the host population that is not safe from parasitoids as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability. Then, we apply the new theory to the following well-known cases: May’s model, [Formula: see text]-model, Hassel and Varley (HV)-model, parasitoid-parasitoid (PP) model and [Formula: see text] model. We use numerical simulations to confirm our theoretical results.