A model for the coupled disease dynamics of HIV and HSV-2 with mixing among and between genders

An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave

Background

The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022-February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province.

Methods

A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters.

Results

The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R0 of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R0k (age group k to age group k), the values of R 0 k (an infected of age group k to the total population) and the values of R ^ 0 k (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship R 0 k > R 0 k > R ^ 0 k was valid. Then, the fluctuating tendencies of effective reproduction number Rt were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19.

Conclusions

This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited.

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.

Dynamics between infectious diseases with two susceptibility conditions: A mathematical model

This paper presents a novel epidemiological transmission model of a population affected by two different susceptible-infected-susceptible infectious diseases. For each disease, individuals fall into one of the two susceptibility conditions in which one of the diseases has the highest occurrence level. This model is unique in assuming that: (a) if an individual is infected by one disease, their susceptibility to the other disease is increased; (b) when an individual recovers from a disease they become less susceptible to it, i.e. they acquire partial immunity. The model captures these two assumptions by utilizing a coupled system of differential equations. Dynamic analysis of the system is based on basic reproductive number theory, and pattern visualization was performed using numerical simulation.

Modeling co-infection of Ixodes tick-borne pathogens

Ticks, including the Ixodes ricinus and Ixodes scapularis hard tick species, are regarded as the most common arthropod vectors of both human and animal diseases in Europe and the United States capable of transmitting a large number of bacteria, viruses and parasites. Since ticks in larval and nymphal stages share the same host community which can harbor multiple pathogens, they may be co-infected with two or more pathogens, with a subsequent high likelihood of co-transmission to humans or animals. This paper is devoted to the modeling of co-infection of tick-borne pathogens, with special focus on the co-infection of Borrelia burgdorferi (agent of Lyme disease) and Babesia microti (agent of human babesiosis). Considering the effect of co-infection, we illustrate that co-infection with B. burgdorferi increases the likelihood of B. microti transmission, by increasing the basic reproduction number of B. microti below the threshold smaller than one to be possibly above the threshold for persistence. The study confirms a mechanism of the ecological fitness paradox, the establishment of B. microti which has weak fitness (basic reproduction number less than one). Furthermore, co-infection could facilitate range expansion of both pathogens.

Modeling Lyme disease transmission

Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A growing body of theoretical models have been proposed to better understand various factors determining the disease risk, which not only enrich our understanding on the ecological cycle of disease transmission but also promote new theoretical developments on model formulation, analysis and simulation. In this paper, we provide a review about the models and results we have obtained recently on modeling and analyzing Lyme disease transmission, with the purpose to highlight various aspects in the ecological cycle of disease transmission to be incorporated, including the growth of ticks with different stages in the life cycle, the seasonality, host diversity, spatial disease pattern due to host short distance movement and bird migration, co-infection with other tick-borne pathogens, and climate change impact.