Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.
The COVID-19 pandemic has proved to be one of the most disruptive public health emergencies in recent memory. Among non-pharmaceutical interventions, social distancing and lockdown measures are some of the most common tools employed by governments around the world to combat the disease. While mathematical models of COVID-19 are ubiquitous, few have leveraged network theory in a general way to explain the mechanics of social distancing. In this paper, we build on existing network models for heterogeneous, clustered networks with random link activation/deletion dynamics to put forth realistic mechanisms of social distancing using piecewise constant activation/deletion rates. We find our models are capable of rich qualitative behavior, and offer meaningful insight with relatively few intervention parameters. In particular, we find that the severity of social distancing interventions and when they begin have more impact than how long it takes for the interventions to take full effect.
Introduction
Despite antiretroviral therapy (ART) scale‐up among people living with HIV (PLHIV), those with advanced HIV disease (AHD) (defined in adults as CD4 count <200 cells/mm
3
or clinical stage 3 or 4), remain at high risk of death from opportunistic infections. The shift from routine baseline CD4 testing towards viral load testing in conjunction with “Test and Treat” has limited AHD identification.
Methods
We used official estimates and existing epidemiological data to project deaths from tuberculosis (TB) and cryptococcal meningitis (CM) among PLHIV‐initiating ART with CD4 <200 cells/mm
3
, in the absence of select World Health Organization recommended diagnostic or therapeutic protocols for patients with AHD. We modelled the reduction in deaths, based on the performance of screening/diagnostic testing and the coverage and efficacy of treatment/preventive therapies for TB and CM. We compared projected TB and CM deaths in the first year of ART from 2019 to 2024, with and without CD4 testing. The analysis was performed for nine countries: South Africa, Kenya, Lesotho, Mozambique, Nigeria, Uganda, Zambia, Zimbabwe and the Democratic Republic of Congo.
Results
The effect of CD4 testing comes through increased identification of AHD and consequent eligibility for protocols for AHD prevention, diagnosis and management; algorithms for CD4 testing avert between 31% and 38% of deaths from TB and CM in the first year of ART. The number of CD4 tests required per death averted varies widely by country from approximately 101 for South Africa to 917 for Kenya.
Conclusions
This analysis supports retaining baseline CD4 testing to avert deaths from TB and CM, the two most deadly opportunistic infections among patients with AHD. However, national programmes will need to weigh the cost of increasing CD4 access against other HIV‐related priorities and allocate resources accordingly.
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