In this paper, the combined influences of biotic interactions, environmental components and harvesting strategy on the spread of Hantavirus are investigated. By employing a multi-species model consisting of (susceptible and infected) rodents and alien species, we show that interspecific competition from alien species has an effect in reducing the spread of infection, and this species could be employed as a potential biocontrol agent. Our analysis using numerical continuation and simulation also reveals the conditions under which Hantavirus infection occurs and disappears as the environmental conditions and the intensity of harvesting change. Without harvesting, infection emerges when environments are conducive. Inclusion of moderate harvesting in favourable environments can lead to disappearance of infection among rodent species. However, as the intensity of harvesting increases, this situation can cause extinction of all rodents species and consequently, jeopardise biodiversity. Overall, our results demonstrate how the interplay of different factors can combine to determine the spread of infectious diseases.
Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups. In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.
Let G be a dihedral group and ??cl G its conjugacy class graph. The Laplacian energy of the graph, LE(??cl G) is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.
Let g be a finite group and s be a subset of g, where s does not include
the identity of g and is inverse closed. A cayley graph of a group g with respect to the
subset s is a graph, where its vertices are the elements of g and two vertices a and b
are connected if ab-1 is in the subset s. The energy of a cayley graph is the sum of all
absolute values of the eigenvalues of its adjacency matrix. In this paper, we consider a
specific subset s = {b, ab, . . . , An-1b} for dihedral groups of order 2n, where n 3 and find
the cayley graph with respect to the set. We also calculate the eigenvalues and compute
the energy of the respected cayley graphs. Finally, the generalization of the energy of the
respected cayley graphs is found.
A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups.
Homotopy continuation methods (HCMs) can be used to find the solutions
of polynomial equations. The advantages of HCMs over classical methods such as the
Newton and bisection methods are that HCMs are able to resolve divergence and starting
value problems. In this paper, we develop Super Ostrowski-HCM as a technique to
overcome the starting value problem. We compare the performance of this proposed
method with Ostrowski-HCM. The results provide evidence of the superiority of Super
Ostrowski-HCM.
Hantaviruses are etiological agents of zoonotic diseases and certain other dis-
eases, which pose a serious threat to human health. When rodent and predator popula-
tions share in an ecology, the competitive force of the populations can lead to a reduction
or elimination of a hantavirus outbreak. The effect of the predator eliminating rodents
and predator populations that tends to reduce or eliminate hantavirus infection is investi-
gated. The existence of several equilibrium points of the model is identified and local and
global stabilities of the model at these equilibrium points are analysed in detail. Numerical
simulations are carried out to illustrate our model results.
Rainfall is an interesting phenomenon to investigate since it is directly related
to all aspects of life on earth. One of the important studies is to investigate and under-
stand the rainfall patterns that occur throughout the year. To identify the pattern, it
requires a rainfall curve to represent daily observation of rainfall received during the year.
Functional data analysis methods are capable to convert discrete data intoa function that
can represent the rainfall curve and as a result, try to describe the hidden patterns of the
rainfall. This study focused on the distribution of daily rainfall amount using functional
data analysis. Fourier basis functions are used for periodic rainfall data. Generalized
cross-validation showed 123 basis functions were sufficient to describe the pattern of daily
rainfall amount. North and west areas of the peninsula show a significant bimodal pattern
with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-
modal patterns that reached a peak in the last three months. Southern areas show more
uniform trends throughout the year. Finally, the functional spatial method is introduced
to overcome the problem of estimating the rainfall curve in the locations with no data
recorded. We use a leave one out cross-validation as a verification method to compare
between the real curve and the predicted curve. We used coefficient of basis functions
to get the predicted curve. It was foundthatthe methods ofspatial prediction can match
up with theexistingspatialpredictionmethodsin terms of accuracy,but it isbetterasthe new
approach provides a simpler calculation.