We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibriu...

Development of resistance to the insecticidal toxins from Bacillus thuringiensis (Bt) in insects is the major threat to the continued success of transgenic Bt crops in agriculture. The fitness of Bt-resistant insects on Bt and non-Bt plants is a key parameter that determines the development of Bt resistance in insect populations. In this study, a comprehensive analysis of the fitness of Bt-resi...

We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number R0. We present that when R0 ≤ 1, there is a unique disease-free equilibrium which is globally asymptotically stable; when R0 > 1, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the...

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibriu...

The impact of an insect-free artificial diet provided at nymphal and/or adult stage upon the developmental rate, life table parameters, and fertility table parameters was examined for Podisus maculiventris (Say). This study showed that when fed an insect-free artificial diet during both the nymphal and adult stage, developmental time was prolonged, preoviposition period was extended, and reprod...

Matrix models are widely used for demographic analysis of age and stage structured biological populations. Dynamic properties of the model can be summarized by the net reproductive rate R (0). In this paper, we introduce a new method to calculate and analyze the net reproductive rate directly from the life cycle graph of the matrix. We show, with examples, how our method of analysis of R (0) ca...

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number R0 of the model is obtained. We investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable, whereas if R0 > 1, then the infection equilibrium is global...

The use of computer algebra software has many applications in diverse fields like epidemiology. This work pretends to show how computer algebra software applications for symbolic computation have a very promissory future in mathematical epidemiology with a concrete problem of this kind. In this case; the basic reproductive rate, corresponding to the propagation of a certain disease inside a cir...

This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection-free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle's invariance principle shows that if the model's basic reproductive number R0 < 1, the infection-free equilibrium point is globa...