Modelling infectious diseases with relapse: a case study of HSV-2

Computational and Theoretical Analysis of the Association Between Gender and HSV-2 Treatment Adherence

Herpes simplex virus type 2 (HSV-2) is the most prevalent sexually transmitted infection in the world, despite the availability of effective anti-viral treatments. A mathematical model to explore the association between gender and HSV-2 treatment adherence is developed. Threshold parameters are determined and stabilities analyzed. Sensitivity analysis of the reproduction number and the numerical simulations suggest that treatment adherence for both females and males are equally important in keeping the reproduction as low as possible. The basic model is then extended to incorporate time-dependent intervention strategies. The Pontryagin's Maximum Principle is used to characterize the optimal level of the controls, and the resulting optimality system is solved numerically.

The basic reproductive number and particle-to-plaque ratio: comparison of these two parameters of viral infectivity

The COVID-19 pandemic has brought more widespread attention to the basic reproductive number (R_o), an epidemiologic measurement. A lesser-known measure of virologic infectivity is the particle-to-plaque ratio (P:PFU). We suggest that comparison between the two parameters may assist in better understanding viral transmission dynamics.

Cost analysis of treatment strategies for the control of HSV-2 infection in the U.S.: A mathematical modeling-based case study

Infection of Herpes Simplex Virus type 2 (HSV-2) is a lifelong sexually transmitted disease. According to the Center for Disease Control and Prevention (CDC), 11.9% of the United States (U.S.) population was infected with HSV-2 in 2015-2016. The HSV-2 pathogen establishes latent infections in neural cells and can reactivate causing lesions later in life, a strategy that increases pathogenicity and allows the virus to evade the immune system. HSV-2 infections are currently treated by Acyclovir only in the non-constitutional stage, marked by genital skin lesions and ulcers. However, patients in the constitutional stage expressing mild and common (with other diseases) symptoms, such as fever, itching and painful urination, remain difficult to detect and are untreated. In this study, we develop and analyze a mathematical model to study the transmission and control of HSV-2 among the U.S. population between the ages of 15-49 when there are options to treat individuals in different stages of their pathogenicity. In particular, the goals of this work are to study the effect on HSV-2 transmission dynamics and to evaluate and compare the cost-effectiveness of treating HSV-2 infections in both constitutional and non-constitutional stages (new strategy) against the current conventional treatment protocol for treating patients in the non-constitutional stage (current strategy). Our results distinguish model parameter regimes where each of the two treatment strategies can optimize the available resources and consequently gives the long-term reduced cost associated with each treatment and incidence. Moreover, we estimated that the public health cost of HSV-2 with the proposed most cost-effective treatment strategy would increase by approximately 1.63% in 4 years of implementation. However, in the same duration, early treatment via the new strategy will reduce HSV-2 incidence by 42.76% yearly and the reproduction number will decrease to 0.84 from its current estimate of 2.5. Thus, the proposed new strategy will be significantly cost-effective in controlling the transmission of HSV-2 if the strategy is properly implemented.

A sexually transmitted infection model with long-term partnerships in homogeneous and heterogenous populations

Population models for sexually transmitted infections frequently use a transmission model that assumes an inherent partnership length of zero. However, in a population with long-term partnerships, the infection status of the partners, the length of the partnership, and the exclusivity of the partnership significantly affect the rate of infection. We develop an autonomous population model that can account for the possibilities of an infection from either a casual sexual partner or a longtime partner who was either infected at the start of the partnership or was newly infected. The impact of the long-term partnerships on the rate of infection is captured by calculating the expected values of the rate of infection from these extended contacts. We present a new method to evaluate partner acquisition rates for casual or long-term partnerships which produces in a more realistic number of lifetime sexual partners. Results include a SI model with different infectiousness levels for the transmission of HIV and HSV-2 with acute and chronic/latent infection stages for homogeneous (MSM) and heterogeneous (WSM-MSW) groups. The accompanying reproduction number and sensitivity studies highlight the impact of both casual and long-term partnerships on infection spread. We construct an autonomous set of equations that handle issues usually ignored by autonomous equations and handled only through simulations or in a non-autonomous form. The autonomous formulation of the model allows for simple numerical computations while incorporating a combination of random instantaneous contacts between individuals and prolonged contacts between specific individuals.