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Leishmaniasis, an infectious disease, manifests itself mostly in two forms, cutaneous leishmaniasis (CL) and, a more severe and potentially deadly form, visceral leishmaniasis (VL). The current control strategy for leishmaniasis relies on chemotherapy drugs such as sodium antimony gluconate (SAG) and meglumine antimoniate (MA). However, all these chemotherapy compounds have poor efficacy, and they are associated with toxicity and other adverse effects, as well as drug resistance. While research in vaccine development for leishmaniasis is continuously progressing, no vaccine is currently available. However, some experimental vaccines such as LEISH-F1+MPL-SE (V) have demonstrated some efficacy when used as drugs for CL patients. In this paper we use a mathematical model to address the following question: To what extent vaccine shots can enhance the efficacy of standard chemotherapy treatment of leishmaniasis? Starting with standard MA treatment of leishmaniasis and combining it with three injections of V , we find, by Day 84, that efficacy increased from 29% to 65–91% depending on the amount of the vaccine. With two or just one injection of V , efficacy is still very high, but there is a definite resurgence of the disease by end-time. [ABSTRACT FROM AUTHOR]

This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov–LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study. [ABSTRACT FROM AUTHOR]

In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number R 0 and the basic immunity reproduction number R 1 . The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number R 01 and immune reproduction number R 02 are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when R 01 < 1 , the virus will be cleared out eventually and the CTL immune response will also disappear; when R 02 < 1 < R 01 , the virus persists within the host, but the CTL immune response disappears eventually; when R 02 > 1 , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given. [ABSTRACT FROM AUTHOR]

This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number R 0 and the humoural immune response activation number R 1 . The results signify that the infection dies out if R 0 ≤ 1. Moreover, the infection persists with inactive immune response if R 1 ≤ 1 < R 0 and with active immune response if R 1 > 1. We illustrate our theoretical results by using numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by their immune response stimulation ratea, we suggest thathas a minimum because a trade-off exists between virulence to the host induced by the pathogen and virulence induced by the immune response. We find that the minimization of the case fatality proportion is an evolutionary stable strategy for the host. [ABSTRACT FROM AUTHOR]

Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves. [ABSTRACT FROM AUTHOR]

HIV-infected patients who receive treatment survive for some years after they have acquired the disease. The received treatment causes sustained reduction of viral reproduction by improving the immune function, leading to prolonged progression period to AIDS development. This prolonged progression period has created variability in survival times that affects estimates produced using mathematical models that do not include delay in disease related mortality. This paper investigates the effect of including delay in AIDS death occurrence in HIV/AIDS transmission models. A simple mathematical model with two stages of HIV progression is developed and extended to include time delay in the occurrence of AIDS deaths. Numerical simulations indicate that time delay changes the mortality curves considerably but has less effect on the proportion of infectives. The study highlights the importance of incorporating delay in models of HIV/AIDS for the production of accurate HIV/AIDS estimates. [ABSTRACT FROM AUTHOR]

This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time since- infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free species coexistence equilibrium. There are also two disease-present equilibria: species one-only disease equilibrium and disease coexistence equilibrium. The existence and stability of these equilibria are governed by six reproduction numbers. Results show that for a nonfatal disease, the disease coexistence equilibrium is stable whenever it exists. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington–DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction numberand the humoral immune response activation numberwhich completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if, then the infection-free equilibrium is globally asymptotically stable (GAS), if, then the chronic-infection equilibrium without humoral immune response is GAS, and if, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations. [ABSTRACT FROM PUBLISHER]

In this paper, on the basis of the simplified two-dimensional virus infection dynamics model, we propose two extended models that aim at incorporating the influence of activation-induced apoptosis which directly affects the population of uninfected cells. The theoretical analysis shows that increasing apoptosis plays a positive role in control of virus infection. However, after being included the third population of cytotoxic T lymphocytes immune response in HIV-infected patients, it shows that depending on intensity of the apoptosis of healthy cells, the apoptosis can either promote or comfort the long-term evolution of HIV infection. Further, the discrete-time delay of apoptosis is incorporated into the pervious model. Stability switching occurs as the time delay in apoptosis increases. Numerical simulations are performed to illustrate the theoretical results and display the different impacts of a delay in apoptosis. [ABSTRACT FROM AUTHOR]

This article is concerned with the dynamics of malaria infection model with diffusion and delay. The disease free threshold ℜ 0 and the immune response threshold value ℜ 1 of the malaria infection are obtained, which characterize the stability of the disease free equilibrium and infection equilibrium (with or without immune response). In addition, fluctuations occur when the model undergoes Hopf bifurcation as the delay passes through a certain critical value τ 0 . In this case, periodic oscillation appears near the positive steady state, which implies the recurrent attacks of disease. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We establish some properties of a within host mathematical model of malaria proposed by Recker et al. [M. Recker et al., Transient cross-reactive immune responses can orchestrate antigenic variation in malaria, Lett. Nature 429 (2004), pp. 555-558; M. Recker and S. Gupta, Conflicting immune responses can prolong the length of infection in Plasmodium falciparum malaria, Bull. Math. Biol. 68 (2006), pp. 821-835.], which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria parasite (Plasmodium falciparum). We show that the model can exhibit a wide variety of dynamical behaviours. We provide criteria for global stability, competitive exclusion and persistence. We also demonstrate that the disease equilibrium can be destabilized by non-symmetric cross-reactive responses. [ABSTRACT FROM AUTHOR]

Chronic fatigue syndrome is a protracted illness condition (lasting even years) appearing with strong flu symptoms and systemic defiances by the immune system. Here, by means of statistical mechanics techniques, we study the most widely accepted picture for its genesis, namely a persistent acute mononucleosis infection, and we show how such infection may drive the immune system towards an out-of-equilibrium metastable state displaying chronic activation of both humoral and cellular responses (a state of full inflammation without a direct ‘causes–effect’ reason). By exploiting a bridge with a neural scenario, we mirror killer lymphocytes TK and B cells to neurons and helper lymphocytes and to synapses, hence showing that the immune system may experience the Pavlov conditional reflex phenomenon: if the exposition to a stimulus (Epstein–Barr virus antigens) lasts for too long, strong internal correlations among B,TK and TH may develop ultimately resulting in a persistent activation even though the stimulus itself is removed. These outcomes are corroborated by several experimental findings. [ABSTRACT FROM PUBLISHER]

We consider a deterministic intra-host model for Plasmodium falciparum (Pf) malaria infection, which accounts for antigenic variation between n clonal variants of PfEMP1 and the corresponding host immune response (IR). Specifically, the model separates the IR into two components, specific and cross-reactive, respectively, in order to demonstrate that the latter can be a mechanism for the sequential appearance of variants observed in actual Pf infections. We show that a strong variant-specific IR relative to the cross-reactive IR favours the asynchronous oscillations (sequential dominance) over the synchronous oscillations in a number of ways. The decay rate of asynchronous oscillations is smaller than that for the synchronous oscillations, allowing for the parasite to survive longer. With the introduction of a delay in the stimulation of the IR, we show that only a small delay is necessary to cause persistent asynchronous oscillations and that a strong variant-specific IR increases the amplitude of the asynchronous oscillations. [ABSTRACT FROM PUBLISHER]

I examine here the effects of host heterogeneity in the growth of immune response on the evolution and co-evolution of virulence. The analysis is based on an extension of the 'nested model' by Gilchrist and Sasaki [Modeling host-parasite coevolution, J. Theor. Biol. 218 (2002), pp. 289-308]; the criteria for host and parasite evolution, in the paradigm of adaptive dynamics, for that model are derived in generality. Host heterogeneity is assumed to be fixed at birth according to a lognormal distribution or to the presence of two discrete types. In both cases, it is found that host heterogeneity determines a dramatic decrease in pathogen virulence, since pathogens will tune to the 'weakest' hosts. Finally we clarify how contrasting results present in the literature are due to different modelling assumptions. [ABSTRACT FROM AUTHOR]

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients. [ABSTRACT FROM AUTHOR]