Inspired by Kouakep , we consider in this note a well-posed model with
differential susceptibility and infectivity adding continuous age structure to
an ODE model for a “Baka” pygmy group in the East of Cameroon (Africa).
Assuming a very low contribution of carriers to infection compared to acute
infection, we estimate a probability $p(a)$ (to develop symptomatic Hepatitis B
state at age $a$) and acute carriers’ transmission rate. The value $R_0 = 2:67 > 1$ of the basic reproduction number estimated from data in the east of Cameroon
confirms that HBV is endemic in the Baka pygmy group.
In this paper, a block coordinate descent method is developed to solve
a linearly constrained separable convex optimization problem. The proposed
method divides the decision variable into a few blocks based on certain rules.
Then the candidate solution is iteratively obtained by updating one block at
each iteration. The problem, whether or not there are overlapping regions
between two immediately adjacent blocks, is investigated. The global convergence of the proposed method is established under some suitable assumptions.
Numerical results show that the proposed method is effective compared with
some “full-type” methods.
A two species commensal symbiosis model with Holling type functional
response and non-selective harvesting in a partial closure is considered. Local
and global stability property of the equilibria are investigated. Depending on
the the area available for capture, we show that the system maybe extinct or
one of the species will be driven to extinction, while the rest one is permanent,
or both of the species coexist in a stable state. The dynamic behaviors of the
system is complicated and sensitive to the fraction of the harvesting area.
In this paper we establish some new dynamic inequalities on time scales
which contain in particular generalizations of integral and discrete inequalities
due to Hardy, Littlewood, Pόlya, D’Apuzzo, Sbordone and Popoli. We also
apply these inequalities to prove a higher integrability theorem for decreasing
functions on time scales.
In this paper, we determine the bounds about Ramsey number $R(W_m, W_n),$ where $W_i$ is a graph obtained from a cycle $C_i$ and an additional vertex by
joining it to every vertex of the cycle $C_i.$ We prove that $3m+1 ≤ R(W_m, W_n) ≤
8m − 3$ for odd $n,$ $m ≥ n ≥ 3,$ $m ≥ 5,$ and $2m + 1 ≤ R(W_m, W_n) ≤ 7m − 2$ for
even $n$ and $m ≥ n + 502.$ Especially, if $m$ is sufficiently large and $n = 3,$ we
have $R(W_m, W_3) = 3m + 1.$
A single-species population model with migrations and harvest between
the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the
equilibria. The research points out, under some suitable conditions, the single-species population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally
asymptotically stable when the harvesting rate exceeds the threshold. Further,
we discuss the practical effects of the protection zones and the harvest. The
main results indicate that the protective zones indeed eliminate the extinction
of the species under some cases, and the theoretical threshold of harvest to
the practical management of the endangered species is provided as well. To
end this contribution and to check the validity of the main results, numerical
simulations are separately carried out to illustrate these results.
In this article, a two-species predator-prey reaction-diffusion system with
Holling type-IV functional response and subject to the homogeneous Neumann
boundary condition is regarded. In the absence of the spatial diffusion, the
local asymptotic stability, the instability and the existence of Hopf bifurcation
of the positive equilibria of the corresponding local system are analyzed in
detail by means of the basic theory for dynamical systems. As well, the effect
of the spatial diffusion on the stability of the positive equilibria is considered
by using the linearized method and analyzing in detail the distribution of roots
in the complex plane of the associated eigenvalue problem. In order to verify
the obtained theoretical predictions, some examples and numerical simulations
are also included by applying the numerical methods to solve the ordinary and
partial differential equations.
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