A malaria model is formulated which includes the enhanced attractiveness of 7 infectious humans to mosquitoes, as result of host manipulation by malaria 8 parasite, and the human behavior, represented by insecticide-treated bed nets 9 usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be 10 possible, which implies that multiple endemic equilibria co-exist with a stable 11 dis...

To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number ?0 for the model, and show that the modeled disease dies out regardless of initi...

‎hepatitis b virus (hbv) infection is a major public health problem in the world today‎. ‎a mathematical model is formulated to describe the spread of hepatitis b‎, ‎which can be controlled by vaccination as well as treatment‎. ‎we study the dynamical behavior of the system with fixed control for both vaccination and treatment‎. ‎the results shows that the dynamics of the model is completely de...

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of ...

We conduct rigorous stability analysis for the well-known cholera model proposed by Codeço [7]. Using theory of monotone dynamical systems, we prove that the endemic equilibrium, when it exists, of the model is globally asymptotically stable, implying the persistence of the disease in the absence of interventions. We then modify Codeço’s model by incorporating various control strategies, and st...

We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R0: If R(0) =/< 1; then the disease-fr...

A mathematical model for the marine bacteriophage infection is proposed and its essential mathematical features are analyzed. Since bacteriophage infection induces bacterial lysis which releases into the marine environment, on the average, 'b' viruses per cell, the parameter b epsilon (1, t infinity) or 'virus replication factor' is chosen as the main parameter on which the dynamics of the infe...

Abstract. In this paper we propose a malaria within-host model with k classes of age for the parasitized red blood cells and n strains for the parasite. We provide a global analysis for this model. A competitive exclusion principle holds. If R0, the basic reproduction number, satisfies R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the contrary if R0 > 1, then g...

In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the...

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is sho...