Bulletin of Mathematical Biology

Mehra, Somya; McCaw, James M.; Flegg, Mark B.; Taylor, Peter G.; Flegg, Jennifer A.

doi: 10.1007/s11538-020-00837-5pmid: 33387082

Malaria is a mosquito-borne disease that, despite intensive control and mitigation initiatives, continues to pose an enormous public health burden. Plasmodium vivax is one of the principal causes of malaria in humans. Antibodies, which play a fundamental role in the host response to P. vivax, are acquired through exposure to the parasite. Here, we introduce a stochastic, within-host model of antibody responses to P. vivax for an individual in a general transmission setting. We begin by developing an epidemiological framework accounting for P. vivax infections resulting from new mosquito bites (primary infections), as well as the activation of dormant-liver stages known as hypnozoites (relapses). By constructing an infinite server queue, we obtain analytic results for the distribution of relapses in a general transmission setting. We then consider a simple model of antibody kinetics, whereby antibodies are boosted with each infection, but are subject to decay over time. By embedding this model for antibody kinetics in the epidemiological framework using a generalised shot noise process, we derive analytic expressions governing the distribution of antibody levels for a single individual in a general transmission setting. Our work provides a means to explore exposure-dependent antibody dynamics for P. vivax, with the potential to address key questions in the context of serological surveillance and acquired immunity.

Alharbi, Mohammed H.; Kribs, Christopher M.

doi: 10.1007/s11538-020-00836-6pmid: 33387065

The influenza virus causes severe respiratory illnesses and deaths worldwide every year. It spreads quickly in an overcrowded area like the annual Hajj pilgrimage in Saudi Arabia. Vaccination is the primary strategy for protection against influenza. Due to the occurrence of antigenic shift and drift of the influenza virus, a mismatch between vaccine strains and circulating strains of influenza may occur. The objective of this study is to assess the impact of mismatch between vaccine strains and circulating strains during Hajj, which brings together individuals from all over the globe. To this end, we develop deterministic mathematical models of influenza with different populations and strains from the northern and southern hemispheres. Our results show that the existence and duration of an influenza outbreak during Hajj depend on vaccine efficacy. In this concern, we discuss four scenarios: vaccine strains for both groups match/mismatch circulating strains, and vaccine strains match their target strains and mismatch the other strains. Further, there is a scenario where a novel pandemic strain arises. Our results show that as long as the influenza vaccines match their target strains, there will be no outbreak of strain H1N1 and only a small outbreak of strain H3N2. Mismatching for non-target strains causes about 10,000 new H3N2 cases, and mismatching for both strains causes about 2,000 more new H1N1 cases and 6,000 additional H3N2 cases during Hajj. Complete mismatch in a pandemic scenario may infect over 342,000 additional pilgrims (13.75%) and cause more cases in their home countries.

Gao, Shasha; Martcheva, Maia; Miao, Hongyu; Rong, Libin

doi: 10.1007/s11538-020-00830-ypmid: 33387083

Vaccination is effective in preventing human papillomavirus (HPV) infection. It is imperative to investigate who should be vaccinated and what the best vaccine distribution strategy is. In this paper, we use a dynamic model to assess HPV vaccination strategies in a heterosexual population combined with gay, bisexual, and other men who have sex with men (MSM). The basic reproduction numbers for heterosexual females, heterosexual males and MSM as well as their average for the total population are obtained. We also derive a threshold parameter, based on basic reproduction numbers, for model analysis. From the analysis and numerical investigations, we have several conclusions. (1) To eliminate HPV infection, the priority of vaccination should be given to MSM, especially in countries that have already achieved high coverage in females. The heterosexual population gets great benefit but MSM only get minor benefit from vaccinating heterosexual females or males. (2) The best vaccination strategy is to vaccinate MSM firstly as many as possible, then heterosexual females, lastly heterosexual males. (3) Given a fixed vaccination coverage of MSM, distributing the remaining vaccines to only heterosexual females or males leads to a similar prevalence in the total population. This prevalence is lower than that when vaccines are distributed to both genders. The evener the distribution, the higher the prevalence in the total population. (4) Vaccination becomes less effective in reducing the prevalence as more vaccines are given. It is more effective to allocate vaccines to a region with lower vaccination coverage. This study provides information that may help policymakers formulate guidelines for vaccine distribution to reduce HPV prevalence on the basis of vaccine availability and prior vaccination coverage. Whether these guidelines are affected when the objective is to reduce HPV-associated cancer incidence remains to be further studied.

Xu, Chaoqun; Yuan, Sanling; Zhang, Tonghua

doi: 10.1007/s11538-020-00843-7pmid: 33387074

Based on the fact that the continuous culture of microorganisms in a chemostat is subject to environmental noises, we present and analyze a stochastic competition chemostat model with general monotonic response functions and differential removal rates. The existence and boundedness of the unique positive solution are first obtained. By defining a stochastic break-even concentration for every species, we prove that at most one competitor survives in the chemostat and the winner has the smallest stochastic break-even concentration, provided its response function satisfies a technical assumption. That is to say, the competitive exclusion principle holds for the stochastic competition chemostat model. Furthermore, we find that the noise experienced by one species is adverse to its growth while may be favorable for the growth of other one species. Namely, the destinies can be exchanged between two microorganism species in the chemostat due to the environmental noise.

Berestycki, Henri; Roquejoffre, Jean-Michel; Rossi, Luca

doi: 10.1007/s11538-020-00826-8pmid: 33315147

It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. The line and the domain interact by constant exchanges of populations. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced Berestycki et al. (J Math Biol 66:743–766, 2013) to describe the enhancement of biological invasions by lines of fast diffusion. We establish the existence of a minimal spreading speed, and we show that it may be quite large, even when the basic reproduction number R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_0$$\end{document} is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line.