Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2206.10548

Nonlinear Dynamic analysis of vector-host model for Zika infection with predatory fish Gambusia Affinis

Sachin Kumar·Shikha Jain
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the present paper, we study the dynamics of a nine compartmental vector-host model for Zika virus infection where the predatory fish Gambusia Affinis is introduced into the system to control the zika infection by preying on the vector. The system has six practically feasible equilibrium points where four of them are disease-free, and the rest are endemic. We discuss the existence and stability conditions for the equilibria. We find that when sexual transmission of zika comes to a halt then in absence of mosquitoes infection cannot persist. Hence, one needs to eradicate mosquitoes to eradicate infection. Moreover, we deduce that in the case of zika infection pushing the basic reproduction number below unity is next to impossible. Therefore, O_0, the mosquito survival threshold parameter, and O, the mosquito survival threshold parameter with predation play a crucial role in getting rid of the infection in respective cases since mosquitoes cannot survive when these are less than unity. Sensitivity analysis shows the importance of reducing mosquito biting rate and mutual contact rates between vector and host. It exhibits the importance of increasing the natural mortality rate of vectors to reduce the basic reproduction number. Numerical simulation shows that when the basic reproduction number is close but greater than unity, the introduction of a small amount of predatory fish Gambusia Affinis can completely swipe off the infection. In case of high transmission or high basic reproduction number, this fish increases the susceptible human population and keeps the infection under control, hence, prohibiting it from becoming an epidemic.

Explore related subjects

math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sachin Kumar, Shikha Jain. 2022-06-21. Nonlinear Dynamic analysis of vector-host model for Zika infection with predatory fish Gambusia Affinis. https://arxiv.org/abs/2206.10548

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Equidistribution of saddle periodic points for Hénon-like maps

We prove that under a natural assumption on the dynamical degrees, the saddle periodic points of a Hénon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of the results of Bedford-Lyubich-Smillie, Dujardin, and Dinh-Sibony along with improvements of their techniques. We also investigate some fine properties of Green currents associated with the map.

math.DS↗
arXiv2026

On dissonance and orthogonal projections of self-conformal measures

Let $μ$ be a self-conformal measure on $\mathbb{R}^d$. We establish conditions for $μ$ under which $\dim(μ*ν) = \min\lbrace d,\dimμ+\dimν\rbrace$ holds when $ν$ is any Ahlfors-regular or self-conformal measure on $\mathbb{R}^d$. Our main result states the following sufficient condition: $μ$ is totally non-linear and not supported on a smooth hypersurface. We also establish sufficient (likely non-sharp) algebraic conditions for self-conformal measures which are not totally non-linear. In addition, we show that $\dim μ\circπ^{-1} = \min\{ k, \dim μ\}$ for every ortohogonal projection $π:\mathbb{R}^d\to\mathbb{R}^k$, $0<k<d$, when either $d=2$ and $μ$ is not self-similar and not supported on a line, or $d\geq 3$ and $μ$ is totally non-linear and not supported on a smooth hypersurface.

math.DS↗
arXiv2026

Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles

Fractional models provide a natural description of systems with memory, but a noninteger derivative should not be introduced solely because a time series is curved or slowly relaxing. We develop an equation-free preliminary screening framework that asks whether a scalar time series produces a multi-horizon k-nearest-neighbor (kNN) profile more compatible with Mittag-Leffler-type behavior than with selected conventional alternatives. In an ideal matched Caputo-relaxation benchmark, the complete generation-kNN-profile-model-comparison pipeline reproduces the expected Mittag-Leffler geometry and recovers the generating order to within approximately $10^{-3}$; this is interpreted as controlled calibration rather than as general fractional-order identification. Under 3% trajectory-specific observational noise, the held-out Mittag-Leffler preference is most consistent when the generating dynamics are well separated from the integer-order limit and becomes progressively less decisive as $α\rightarrow1$. The fitted order $α_{\mathrm{fit}}$, however, shows substantially larger realization-to-realization variability. Thus, relative model compatibility is more robust than single-realization order estimation in the present noisy benchmark. Noise-free nonfractional controls show a separate limitation of specificity: a stretched exponential can generate a strongly Mittag-Leffler-compatible profile, whereas inclusion of the generating rational/Hill family recovers that family and its parameters to numerical precision in the matched setting. A positive Mittag-Leffler-versus-exponential screen therefore does not uniquely establish fractional origin. A fractional chaotic system is treated only as an exploratory extension: the Mittag-Leffler growth family gives lower finite-window RMSE than exponential and logistic/saturating alternatives over the detected pre-transition interval.

math.DS↗