Introduction
Inadequate physical activity (PA) is now recognized as the fourth leading risk factor for global human mortality, posing greater harm than is widely acknowledged ( Blair, 2009 ). The mantra “Exercise is medicine” has been adopted in numerous countries, aiming to enhance people’s physical fitness through exercise. This initiative supports the concept of “healthy aging”, decelerating the aging process and the progression of diseases ( Galloza, Castillo & Micheo, 2017 ). Regular physical activity is deemed safe for both the robust and the frail among middle-aged and elderly populations. Engaging in a spectrum of activities, ranging from low-intensity walking to more strenuous exercises and resistance training, can lower the risk of infectious diseases such as the flu, pneumonia, and pneumococcal pneumonia. Moreover, regular PA boosts immunoprotection by improving pathogen surveillance and increasing the levels of CD4T helper cells and salivary immunoglobulin IgA ( Hamer, O’Donovan & Stamatakis, 2019 ; Kunutsor, Laukkanen & Laukkanen, 2017 ; Zhao et al., 2020 ). Epidemiological studies have shown that middle-aged and elderly individuals reap significant health benefits from increased PA and achieving moderate-to-high levels of physical fitness ( Morss et al., 2004 ). There is a notable inverse correlation between PA levels and the prevalence of various chronic diseases, with the most substantial health benefits occurring at certain intensities or durations of PA ( Sattelmair et al., 2011 ).

As science and technology continue to advance, and data processing and collection become more systematic, it is now possible to analyze the relationship between exercise volume, intensity, duration, and the threshold intervals for promoting health ( Morss et al., 2004 ; Sattelmair et al., 2011 ). To explain this relationship objectively, an increasing number of researchers have started investigating the dose–response relationship between PA levels and health. In the 1990s, Nieman (1994) proposed a “J” model to describe the dose–response relationship between exercise load (a combination of intensity and volume) and upper respiratory tract infections. On the basis of their analysis in experimental animals, they concluded that based on the current experimental data and study design, a “J” curve-based model is a good method for predicting and analyzing the risk of upper respiratory tract infections in moderately active individuals. In a one-year randomized controlled trial of postmenopausal women, Chubak et al. (2006) found that moderate-intensity exercise training for one year reduced the incidence of colds in postmenopausal women. This reveals a dose–response relationship between exercise intensity and illness. In a separate epidemiological study, Fondell et al. (2011) examined the correlation between PA levels, perceived stress, and the incidence of self-reported urinary tract infections. They discovered that high levels of PA were linked to a lower risk of self-reported urinary tract infections compared to low levels of PA. This association was found to be stronger in individuals who reported high levels of stress, particularly in males, but not in those with low levels of stress. For both men and women, engaging in high-intensity PA is associated with a lower risk of contracting a urinary tract infection ( Fondell et al., 2011 ). Pandey et al. (2015) reported that there is an inverse dose–response relationship between PA and heart failure risk. Doses of PA that exceed the guideline-recommended minimum levels may be needed to achieve a greater reduction in heart failure risk. Physical activity during leisure time (LTPA) was effective in reducing the probability of developing metabolic syndrome (MetS). Zhang et al. (2017) found that There was a negative linear dose–response relationship between LTPA and MetS, with an 8% reduction in the risk of MetS for every 10 metabolic equivalent (MET) h/week increase in physical activity in participants. According to the World Health Organization (WHO) individuals aged 65 years and older should engage in 150 min of moderate-intensity aerobic exercise or 75 min of vigorous-intensity aerobic exercise per week, in addition to muscle strength training for more than two days per week. This can effectively reduce their risk of disease ( Hamer, O’Donovan & Stamatakis, 2019 ). There is a demonstrable quantitative relationship between exercise intensity and its health and fitness benefits, with exercise intensity being crucial for regulating physiological stress and maximizing the health benefits of daily PA ( Gonzales et al., 2021 ). In summary, these randomised controlled trials and epidemiological investigations have found a “dose effect” relationship between specific physical activity and the risk of disease.

While numerous studies have examined the duration and frequency of exercise across different populations, the focus has predominantly been on developed countries ( Csizmadi et al., 2011 ; Steeves et al., 2018 ). These studies have highlighted a strong link between moderate- to high-frequency exercise and a lower risk of colds ( Chubak et al., 2006 ; Nieman et al., 2011 ). However, it is crucial to acknowledge that these findings, being limited to developed countries, might not universally apply. In China, the largest developing country, research on this subject is scarce, with existing studies mainly exploring the relationship between economic status and cold frequency or characterizing the PA patterns of the elderly Chinese population ( Jurj et al., 2007 ; Zhou et al., 2018 ). To date, there has been no definitive conclusion on how cumulative weekly PA levels impact the risk of colds in middle-aged and elderly individuals, leaving a significant gap in our understanding of the optimal exercise thresholds for maintaining health.

The purpose of this study is to investigate the dose–response relationship between weekly physical activity level and the frequency of colds among middle-aged and elderly individuals over 40 years old in China. It can provide a reference for middle-aged and elderly individuals regarding their physical activity levels in the future.