In this paper, we analyzed dynamics of malaria disease by a compartment model involving ordinary differential equations for the human and mosquito populations. An equivalent system is obtained, which has two equilibriums: a disease-free equilibrium and an endemic equilibrium. The stability of these two equilibriums is controlled by the basic reproduction number . In this model the disease-free equilibrium state is stable if and if , the endemic equilibrium stable. The analytical predictions are conformed by numerical simulation and graphical results.
The purpose of this paper is to prove a common fixed point theorem on fuzzy metric space using the notion of semi compatibility, our result generalize the result of Som [8]. Also, we are giving an example that make strong to our result. ) {Tx n }→x, {Sx n }→x then {STx n }→ Tx as n→∞ hold. However (b) implies (a) taking {x n }→y and x = Ty = Sy. So, here we define semi compatibility by condition (b) only. In this paper we used the concept of semi compatible mappings to prove further resuts.
In the present paper, we proposed and analyzed an SIQR compartment model. Determine the steady state of the model and Stability analysis is carried out. Equilibrium analysis is presented and it is found that in each case the equilibrium Points are locally asymptotically stable under certain conditions The stability of the equilibriums are studied by using the Routh-Hurwitz criteria.
The present paper deals with the idea of quasi-pseudo metric space in fuzzy mapping. We extend some earlier result of Singh and Talwar [9].Zadeh[11] stimulated a great interest among mathematicians, engineers, biologists, economists, psychologists and experts in other areas who use mathematical methods in their research. The concept of Fuzzy Mappings was first introduced by Heilpern [3], who has proved a fixed point theorem for fuzzy contraction mappings. Afterwards the result of Heilpern [3], was extended by Bose and Sahani [1], to pair of generalized fuzzy contraction mappings. Recently, Gregori and Pastor [2], proved a fixed point theorem for fuzzy contraction mappings in left K sequentially complete quasi-pseudo metric spaces. In 2005, Sahin et. al [7] obtained common fixed point theorem for pairs of fuzzy mappings in left K sequentially complete quasi-pseudo metric spaces and right K sequentially complete quasi-pseudo metric spaces. In 2008, Pathak and Singh [6] obtained common fixed point theorems for contractive type fuzzy mappings in quasi-pseudo metric space which extend and generalize the result of Sahin et.al [7]. In 2010, Elida and Arben [4], prove common fixed point theorems for a class of fuzzy mappings in symth complete quasi metric space. In 2011, Elida and Arben [5], proved common fixed point theorem for fuzzy weakly contractive mappings in the settings of quasi metric spaces.
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