Effect of innate and adaptive immune mechanisms on treatment regimens in an AIDS-related Kaposi's Sarcoma model.

Kaposi Sarcoma (KS) is the most common AIDS-defining cancer, even as HIV-positive people live longer. Like other herpesviruses, human herpesvirus-8 (HHV-8) establishes a lifelong infection of the host that in association with HIV infection may develop at any time during the illness. With the increasing global incidence of KS, there is an urgent need of designing optimal therapeutic strategies for HHV-8-related infections. Here we formulate two models with innate and adaptive immune mechanisms, relevant for non-AIDS KS (NAKS) and AIDS-KS, where the initial condition of the second model is given by the equilibrium state of the first one. For the model with innate mechanism (MIM), we define an infectivity resistance threshold that will determine whether the primary HHV-8 infection of B-cells will progress to secondary infection of progenitor cells, a concept relevant for viral carriers in the asymptomatic phase. The optimal control strategy has been employed to obtain treatment efficacy in case of a combined antiretroviral therapy (cART). For the MIM we have shown that KS therapy alone is capable of reducing the HHV-8 load. In the model with adaptive mechanism (MAM), we show that if cART is administered at optimal levels, that is, 0.48 for protease inhibitors, 0.79 for reverse transcriptase inhibitors and 0.25 for KS therapy, both HIV-1 and HHV-8 can be reduced. The predictions of these mathematical models have the potential to offer more effective therapeutic interventions in the treatment of NAKS and AIDS-KS.

Stochastic plant-herbivore interaction model with Allee effect.

Environmental noises often affect population dynamics, and hence many benefits are gained in using stochastic models since real life is full of stochasticity and randomness. In this paper a stochastic extension of a model by Asfaw et al. (Int J Biomath 11:1850057, 2018) is considered. Due to the non-linearity of the model, first, a simplified stochastic plant-herbivore model is formulated and analyzed for its global Lipschitz continuity, positivity, existence and uniqueness of solutions. Second, the analysis is extended to a more complex and realistic model. Numerical simulations using Euler-Maruyama method are employed to demonstrate the long term dynamics. It was found that the noise added to the herbivore population resulted more change in the dynamics than the noise added to the plant population (food source). Ignoring the environmental noise could make the land management and wild life conservation not to maintain their goals.

Can malaria parasite pathogenesis be prevented by treatment with tumor necrosis factor-alpha?

We consider a model incorporating the influence of innate and adaptive immune responses on malaria pathogenesis. By calculating the model reproduction number for a special representation of cytokine interaction, we have shown that the cytokine tumour necrosis factor-α can be administered to inhibit malaria infection. We have also found that if the cytokine F ∗ and a generic drug of efficacy ε are administered as dual therapy then clearance of the parasite can be achieved even for a generic drug of low efficacy. Our study is recommending administration of dual therapy as a strategy to prevent parasites from developing resistance to malaria treatment drugs.

Effects of replicative fitness on competing HIV strains.

We develop an n-strain model to show the effects of replicative fitness of competing viral strains exerting selective density-dependant infective pressure on each other. A two strain model is used to illustrate the results. A perturbation technique and numerical simulations were used to establish the existence and stability of steady states. More than one infected steady states governed by the replicative fitness resulted from the model exhibiting either strain replacement or co-infection. We found that the presence of two or more HIV strains could result in a disease-free state that, in general, is not globally stable.

A two-sex model for the influence of heavy alcohol consumption on the spread of HIV/AIDS.

The HIV/AIDS epidemic, one of the leading public health problems to have affected sub-Sahara Africa, is a multifaceted problem with social, behavioral and biological aspects. In the absence of a cure, behavioral change has been advocated as an intervention strategy for reversing the epidemic. Empirical studies have found heavy alcohol consumption to be a fueling factor for HIV/AIDS infection and progression. Previously [20], we formulated and analyzed a one-sex deterministic model to capture the dynamics of this deadly interaction. But, since alcohol drinking habits, consequent risky sexual practices, alcohol-induced immune suppression, etc., can be different for men and women, the primary objective of our present paper is to construct a two-sex model aimed at shedding light on how both sexes, with varying heavy alcohol consumption trends, contribute differently to the HIV/AIDS spread. Based on numerical simulations, supported by the UNAIDS epidemiological software SPECTRUM and using the available data, our study identifies heavy drinking among men and women to be a major driving force for HIV/AIDS in Botswana and sub-Sahara Africa and quantifies its hazardous outcomes in terms of increased number of active TB cases and economic burden caused by increased need for AntiRetroviral Therapy (ART). Our simulations point to the heavy-drinking habits of men as a major reason for the continuing disproportionate impact of HIV/AIDS on women in sub-Sahara Africa. Our analysis has revealed the possibility of the phenomenon of backward bifurcation. In contrast to the result in some HIV vaccination models [52], backward bifurcation in our model is not removed by replacing the corresponding standard incidence function with a mass action incidence, but is removed by merging the two susceptible classes of the same sex into one, i.e., by ignoring acquisition of, and ongoing recovery from, heavy-drinking habits among the susceptible population.

HIV model incorporating differential progression for treatment-naive and treatment-experienced infectives.

We formulate an HIV/AIDS deterministic model which incorporates differential infectivity and disease progression for treatment-naive and treatment-experienced HIV/AIDS infectives. To illustrate our model, we have applied it to estimate adult HIV prevalence, the HIV population, the number of new infectives and the number of AIDS deaths for Botswana for the period 1984 to 2012. It is found that the prevalence peaked in the year 2000 and the HIV population is now decreasing. We have also found that under the current conditions, the reproduction number is Rc approximately 13, which is less than the 2004 estimate of Rc approximately equal 4 by [11] and [13]. The results in this study suggest that the HAART program has yielded positive results for Botswana.

The effects of vertical transmission on the spread of hiv/aids in the presence of treatment.

In this study, we develop a model that incorporates treatment of both juveniles who were infected with HIV/AIDS through vertical transmission and HIV/AIDS-infected adults. We derive conditions under which the burden of HIV/AIDS can be reduced in the population both in the absence of and in the presence of vertical transmission. We have determined the critical threshold parameter (R(*)(v)), which represents the demographic replacement of infectives through vertical transmission, below which treated infected juveniles can reach adulthood without causing an epidemic. Five countries in sub-Saharan Africa are used to illustrate our results. We have concluded that R(*)(v) is dependent on the current prevalence rate but that a significant proportion of infected juveniles receiving treatment can reach adulthood without causing an epidemic.