Mathematical modeling of chickenpox in Phuket: Efficacy of precautionary measures and bifurcation analysis

A predator-prey model with additive Allee effect and intraspecific competition on predator involving Atangana-Baleanu-Caputo derivative

Robust synchronization of multi-weighted fractional order complex dynamical networks under nonlinear coupling via non-fragile control with leakage and constant delays

Complex dynamics of a non-smooth temperature-sensitive memristive Wilson neuron model

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.

A Fractional-Order Density-Dependent Mathematical Model to Find the Better Strain of Wolbachia

We established a mathematical model based on the sense of biological survey in the field of agriculture and introduced various control methods on how to prevent the crops from destructive pests. Basically, there are two main stages in the life cycle of natural enemies like insects: mature and immature. Here, we construct a food chain model of plant pest natural enemy. In natural enemies, there are two stages of construction. Also, we consider three classes of diseases in the pest population, namely, susceptible, exposed, and infectious in this proposed work. In order to categorize the considered models into the class of Impulsive Differential Equations (IDEs), in our study, we specifically consider two ecosystems, which define the impact of control mechanisms on the impulsive releasing of virus particle natural enemies and infectious pests at particular time. Additionally, the importance of spraying virus particles in pest control is discussed; then, we obtain two types of periodic solutions for the system, namely, plant pest extinction and pest extinction. By utilizing the small amplitude perturbation techniques and Floquet theory of the impulsive equation, we obtain the local stability of both periodic solutions. Moreover, the comparison technique of IDE shows the sufficient conditions for the global attractivity of a pest extinction periodic solution. With the assistance of the comparison results, we draw a numerical calculation for the addressed models. Finally, we extend the study of the two models for pest management models: with and without the existence of virus particle.

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An Integrated Eco-Epidemiological Plant Pest Natural Enemy Differential Equation Model with Various Impulsive Strategies

Mathematical modeling on co-infection: transmission dynamics of Zika virus and Dengue fever

The exotic beetle Zygogramma bicolorata is an effective biological control agent of Parthenium hysterophorus in India as it feeds mainly on this weed. In the present study the stress of high and low temperature (200C & 350C) as compared to normal (Control at 270C) on the reproductive performance and different life cycle stages of the Mexican beetle Zygograma bicolorata was investigated. Potential fecundity (number of eggs matured) and realized fecundity (number of eggs laid) are both influenced by temperature variation. Fecundity and percent egg viability increased significantly with increase in the temperature from 200C to 27oC and thereafter declined with further increase in temperature. The development and survival of different life stages were also recorded and egg hatching (in days), larval period, pupal period were affected by the temperature variation. The ideal temperature range for the maximum egg laying, high percentage of egg hatching, maximum survival and complete development were recorded at 270C. These findings may be useful in mass rearing of the beetle in laboratory condition.

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Influence of temperature variation on reproductive attributes of zygograma bicolorata (coleoptera: chrysomelidae) a potential biocontrol agent of weed parthenium hystorophorus

Rina Saha Manoj Bangadkar I. A. Raja Rina Saha Manoj Bangadkar I. A. Raja

Papers

An Integrated Eco-Epidemiological Plant Pest Natural Enemy Differential Equation Model with Various Impulsive Strategies

Mathematical modeling of chickenpox in Phuket: Efficacy of precautionary measures and bifurcation analysis

Mathematical modeling on co-infection: transmission dynamics of Zika virus and Dengue fever

Influence of temperature variation on reproductive attributes of zygograma bicolorata (coleoptera: chrysomelidae) a potential biocontrol agent of weed parthenium hystorophorus