Demography is one of the factors determining and influencing the geopolitical balance of power in international relations. Politicians are the main actors in international relations, but powerful human dynamics are at work behind them. The study of geopolitics describes these dynamics, linked to human and physical geography. In the evolution of great power competition, economic, military and technological factors are taken into account, but the importance of demographic trends, which will play a key role in the struggle for world power, is often underestimated as a political and geopolitical factor. Demography works over long periods of time, i.e., over generations. The aim of this paper is to illustrate the importance of the above theory by looking at the demographic shock that France experienced in the 19th century and the geopolitical resulting consequences. As a result of this demographic shock, France lost its supremacy as the most populous country in Europe and was definitively overtaken by Germany. It is a scenario that can be useful for understanding the evolution of demographic competition in the 21st century, such as that of China versus India. In 2023, China will lose its supremacy as the world's most populous country to India. This will be the first time that China has lost its primacy since the United Nations began tracking global demographic trends in 1950. China, like France in the past, is in danger of never catching up with its demographic disadvantage. History suggests that once a country crosses the threshold of negative population growth, regardless of the differences in national experiences, there is little that its government can do to reverse it.
Citation: Giuseppe Terranova. Demography, geopolitics and great power: A lesson from the past[J]. AIMS Geosciences, 2023, 9(4): 798-809. doi: 10.3934/geosci.2023043
[1] | Arvind Kumar Misra, Rajanish Kumar Rai, Yasuhiro Takeuchi . Modeling the control of infectious diseases: Effects of TV and social media advertisements. Mathematical Biosciences and Engineering, 2018, 15(6): 1315-1343. doi: 10.3934/mbe.2018061 |
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[9] | Jingli Xie, Hongli Guo, Meiyang Zhang . Dynamics of an SEIR model with media coverage mediated nonlinear infectious force. Mathematical Biosciences and Engineering, 2023, 20(8): 14616-14633. doi: 10.3934/mbe.2023654 |
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Demography is one of the factors determining and influencing the geopolitical balance of power in international relations. Politicians are the main actors in international relations, but powerful human dynamics are at work behind them. The study of geopolitics describes these dynamics, linked to human and physical geography. In the evolution of great power competition, economic, military and technological factors are taken into account, but the importance of demographic trends, which will play a key role in the struggle for world power, is often underestimated as a political and geopolitical factor. Demography works over long periods of time, i.e., over generations. The aim of this paper is to illustrate the importance of the above theory by looking at the demographic shock that France experienced in the 19th century and the geopolitical resulting consequences. As a result of this demographic shock, France lost its supremacy as the most populous country in Europe and was definitively overtaken by Germany. It is a scenario that can be useful for understanding the evolution of demographic competition in the 21st century, such as that of China versus India. In 2023, China will lose its supremacy as the world's most populous country to India. This will be the first time that China has lost its primacy since the United Nations began tracking global demographic trends in 1950. China, like France in the past, is in danger of never catching up with its demographic disadvantage. History suggests that once a country crosses the threshold of negative population growth, regardless of the differences in national experiences, there is little that its government can do to reverse it.
Media coverage, awareness campaign or programs, and public education have played an important and significant role in the control and prevention of the spread of infectious diseases, such as influenza, AIDS/HIV, and SARS. It has been shown that media coverage may change individuals' behavior, while the epidemic is in progress, such as reducing the individuals' contacts or using more safer prevention strategies, to reduce the risk of getting infected [1,2,3,19]. Indeed, people's response to the threat of disease is dependent on their perception of risk, which is influenced by public and private information disseminated widely by the media [33]. In a recent study for outbreaks of infectious diseases with high morbidity and mortality, Mummert and Weiss showed that individuals closely follow media reports of the outbreak, and that many will attempt to minimize contacts with other individuals in order to protect themselves from infection [30]. Therefore, understanding the effects of behavior changes due to influences of media coverage and awareness programs can help guide more effective media plans and strategies on the control and preventions of diseases.
Various mathematical models have been formulated for such purposes. The media coverage and awareness programs can be incorporated into disease transmission models in a more explicit way where an equation or equations for the media coverage or awareness programs are included into compartmental disease models [8,28,29,0]. They can also be incorporated implicitly by being connected to individuals' behavior changes which are expressed in the contact rates or other model terms and therefore the infection or incidence rates [10,30,33,35,36,37]. In the latter case, several types of media influence-dependent incidence rates have been proposed to reflect the influences of media coverage. They include the reduction in contacts due to behavioral change when the number of infectious individuals increases, and have used such forms as
Employing distinct functions for media coverage in similar disease models can certainly exhibit different model dynamics. The following three distinct functions to present the effects of mass media are identified and compared from various perspectives in [9]
f(I,p1)=e−p1γI,f(I,p2)=11+p2I2,f(I,p3)=1−1p3+I. |
It is demonstrated in [9] that, based on a same SEIR (susceptible-exposed-infectious-recovered) compartmental model, the epidemic curves and key epidemic measurements vary depending on the media functions chosen. In particular, even the models with the distinct media functions have a very similar shape and the same basic reproductive number
We note that while the influence of media coverage is an important factor in the spread of diseases, it usually does not impact the disease transmissions so rapidly or sensitively as some other factors and thus the reactions to the media coverage from the public are normally slow and delayed. Susceptible individuals may lack the knowledge or information and tend to ignore the media coverage or awareness campaigns when a disease first spreads, especially for those less fatal diseases. As the disease spreads more widely or more severely, the public pays more attention to the media coverage, and individuals then more seriously change their behavior. As a result, the media impact gradually becomes more significant as the infections are clearly increased. Apparently, most of the media functions used in many studies mentioned above, such as
f″(I){<0,for I<1/√a,>0,for I>1/√a, |
and may thus be used more appropriately to reflect the individuals slow reactions.
To explore the dynamic features of the disease models with this media function and investigate its possibly different impact on the disease transmissions, we consider an SEI model with media coverage or awareness programs in this paper. We assume that the media coverage or awareness programs directly affect individuals' contact rates. We first present the model system with its basic dynamical properties in Section 2. We then derive a formula for the reproductive number
Considering the transmission of infectious diseases in some regions, we divide the population into the groups of susceptible individuals, denoted by
dSdt=bS(1−SK)−ΛS,dEdt=ΛS−(c+d)E,dIdt=cE−γI, | (1) |
where
The infection rate is given by
Λ=βξIN |
where
r(I)=m1+aI2, |
where
dSdt=bS(1−SK)−μI1+aI2S,dEdt=μI1+aI2S−(c+d)E,dIdt=cE−γI, | (2) |
where we write
Define region
D:={(S,E,I)∈IR3:S,E,I≥0,S+E+I≤bKl}, |
where
We first derive a formula for the basic reproduction number,
F=(μSI1+aI200),V=((c+d)E−cE+γI−bS(1−SK)+μSI1+aI2). |
The infected compartments are
F=(0μK00),V=(c+d0−cγ), |
FV−1=1γ(c+d)⋅(μKcμK(c+d)00). |
Hence the basic reproduction number for system (2) is
ℜ0=ρ(FV−1)=μcKγ(c+d), |
and then from [34], the disease-free equilibrium
We next show that
Theorem 3.1. For model (2), if
Proof. We define a Lyapunov functional for system (2) as
U(t):=S(t)−KlnS(t)K−K+E(t)+c+dcI(t). |
Thus we have
dUdt|(2)=S−KS⋅(bS(1−SK)−μSI1+aI2)+μSI1+aI2−(c+d)E+c+dc⋅(cE−γI)=−bK⋅(S−K)2+μKI1+aI2−γ(c+d)c⋅I=−bK⋅(S−K)2+γ(c+d)c⋅(ℜ01+aI2−1)⋅I≤0. |
Set
A0={(S,E,I)∈D|U′=0}. |
Then
S(t)=K, I(t)=0. | (3) |
Substituting (3) into the second equation of system (2) then yields
We further show that system (2) is permanence if the basic reproduction number
Theorem 3.2. Assume
limt→∞inf(S(t),E(t),I(t))≥η:=(ϵ,ϵ,ϵ), |
and thus system (2) is permanence.
Proof. Define sets
X:={(S,E,I):S≥0,E≥0,I≥0}, |
X0:={(S,E,I)∈X:S>0,E>0,I>0}, |
and
∂X0:=X∖X0. |
Let
Define
Ω∂:={ϕ(t)∈∂X0,∀t≥0}. |
We now claim that
Ω∂={ϕ(t)∈∂X0:E(t)=0 and I(t)=0,∀t≥0}. | (4) |
Let
Assume otherwise. Then there exists nonnegative constant
On the other hand, by the last equation in (2), we have
We now let
Ψ0:=⋂x∈Z0w(x). |
Here
Since
Next, we prove that
By the first equation of (2), we have
˙SS=b(1−SK)−μI1+aI2>b(1−ϵ1K)−μϵ1>0, t>T0, |
where we let
Next, we prove
By the second equation and the third equation in (2) and
(˙E˙I)=(μSI1+aI2−(c+d)EcE−γI)≥(−(c+d)μ(K−ϵ2)c−γ)⋅(EI). |
Let
A=(−(c+d)μ(K−ϵ2)c−γ). |
The characteristic polynomial of
|λ+(c+d)−μ(K−ϵ2)−cλ+γ|=λ2+(c+d+γ)λ+(c+d)γ−cμ(K−ϵ2). |
As
Letting the right hand side of (2) equal zero, we find that the origin
From model (2), an endemic equilibrium satisfies the following equations:
bS(1−SK)=μSI1+aI2=(c+d)γIc, | (5) |
which leads to
μS−α(1+aI2)=0, | (6) |
bS(K−S)−αKI=0, | (7) |
where we write
Solving (6) for
I=f1(S)=√μaα(S−αμ), | (8) |
which is a parabola for
I=f2(S)=√bKα(K−S), | (9) |
for
Clearly, the curves of functions
F(I)=I4+1a(2−ℜ0)I2+μℜ0a2bI+1a2(1−ℜ0)=0. | (10) |
Notice that as
We first give a simple lemma for convenience.
Lemma 4.1. The cubic equation
H(x):=Ax3−Bx+C=0, |
with
27AC2>4B3, 27AC2=4B3, 27AC2<4B3, |
respectively.
Proof. Function
H(ˉx)=13ˉx(3Aˉx2−B)+13Bˉx−Bˉx+C=C−23Bˉx. |
Then the conclusion follows directly by substituting
Apply Lemma 4.1 to
F′(I)=4I3+2a(2−ℜ0)I+μℜ0a2b=0 | (11) |
and define
ah:=27μ2ℜ208b2(ℜ0−2)3. | (12) |
Then
Assume
We consider the case where
F(I)= I(I3+12a(2−ℜ0)I+μℜ04a2b)+12a(2−ℜ0)I2+3μℜ04a2bI+1a2(1−ℜ0)=12a(2−ℜ0)I2+3μℜ04a2bI+1a2(1−ℜ0):=G(I). |
It follows from
(3μℜ04a2b)2=4(12a(2−ℜ0)1a2(1−ℜ0)), |
that is
a=ac:=9μ2ℜ2032b2(2−ℜ0)(1−ℜ0). | (13) |
Under condition (13), the unique positive solution to
I=3μℜ04a2b2a2(ℜ0−2)=3μℜ04ab(ℜ0−2). | (14) |
Substituting (14) into
(3μℜ04ab(ℜ0−2))3+2−ℜ02a3μℜ04ab(ℜ0−2)+μℜ04a2b=(3μℜ02ab(ℜ0−2))3−μℜ02a2b=0, |
or equivalently,
a=27μ2ℜ208b2(ℜ0−2)3=ah. |
That is, there exists a positive solution to both
Under the assumption of
Theorem 4.2. Assume
Proposition 1. Consider model (2) with all parameters positive. Clearly we could always find parameter
In this section, we study the stability and Hopf bifurcation of the endemic equilibria and determine how the media impact can influence the periods of the oscillations of disease transmissions.
The case
λ3+(c+d+γ+bℜ0)λ2+bℜ0(c+d+γ)λ+bγ(c+d)(1−1ℜ0)=0. |
Let
RH0=12[1+(c+d+γ)2γ(c+d)+√1+2(c+d+γ)(2b+c+d+γ)γ(c+d)+(c+d+γ)4γ2(c+d)2]. | (15) |
Obviously, for any positive parameters we have
When
JE2=(−bS∗K0μKℜ0−2μK2ℜ20S∗b(1−S∗K)−(c+d)−μKℜ0+2μK2ℜ20S∗0c−γ), |
and the characteristic equation of
λ3+a2λ2+a1λ+a0=0, | (16) |
where
a2=c+d+γ+bS∗K,a1=bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗. | (17) |
The coordinates of the endemic equilibrium
S∗=S∗0+aS∗1+O(a2) | (18) |
where particularly, by (5) we have
S∗0=Kℜ0, S∗1=S∗0bμ(1−1ℜ0). | (19) |
Next, we study the impact of the media coverage on the dynamics of the disease transmissions, and consider the case of
It is easy to verify that (16) has a pair of purely imaginary roots if and only if
Δ=a1a2−a0. | (20) |
If
Δ=a1a2−a0=(c+d+γ+bS∗K)[bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗]−μcbS∗ℜ0−bc(2S∗K−1)(μKℜ0−2μK2ℜ20S∗)=1ℜ20S∗[bℜ20S∗2K(c+d+γ)2+2μcKℜ0S∗(c+d+γ)−2μcK2(c+d+γ)+b2ℜ20S∗3K2(c+d+γ)+bμc(Kℜ0S∗+2KS∗−ℜ0S∗2−2K2)]. | (21) |
By (17), (18) and (19), we have
Δ=1ℜ50S∗⋅(˜Δ(a,ℜ0)+O(a2)), | (22) |
where
˜Δ(a,ℜ0)=bℜ50(c+d+γ)2K[K2ℜ20+2abK2μℜ20(1−1ℜ0)]+2μcKℜ40(c+d+γ)[Kℜ0+abKμℜ0(1−1ℜ0)]−2μcK2ℜ30(c+d+γ)+b2ℜ50(c+d+γ)K2[K3ℜ30+3abK3μℜ30(1−1ℜ0)]+bcμℜ30[(2K+Kℜ0)[Kℜ0+abKμℜ0(1−1ℜ0)]−2K2−ℜ10[K2ℜ20+2abK2μℜ20(1−1ℜ0)]]=ℜ30[bK(c+d+γ)2(1+2abμ)+2cK2ab(c+d+γ)+bcμK2(abμ−1)]+ℜ20[−2ab2K(c+d+γ)2μ+b2K(c+d+γ)(1+3abμ)−2abcK2(c+d+γ)−ab2cK2+bμcK2]+ℜ0[−3ab3K(c+d+γ)μ]. | (23) |
It is not difficult to verify that
ω2=bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗. | (24) |
If the parameters
Lemma 4.3. Consider
ℜ0(a)=RH0+aRH1+O(a2), | (25) |
where
R2H0γ(c+d)−RH0[(c+d+γ)2+γ(c+d)]−b(c+d+γ)=0 | (26) |
and
RH1=−R2H0[2b2K(c+d+γ)2μ+2bcK2(c+d+γ)+b2cK2]3RH0[bK(c+d+γ)2−bμcK2]+2[b2K(c+d+γ)+bμcK2]+RH0[2b2K(c+d+γ)2μ−3b3K(c+d+γ)μ+2bcK2(c+d+γ)+b2cK2]3RH0[bK(c+d+γ)2−bμcK2]+2[b2K(c+d+γ)+bμcK2]+3b3K(c+d+γ)μ3RH0[bK(c+d+γ)2−bμcK2]+2[b2K(c+d+γ)+bμcK2]. | (27) |
Proof. Note that
˜Δ(0,RH0)=R3H0[bK(c+d+γ)2−bcK2μ]+R2H0[b2K(c+d+γ)+bcK2μ]=0 |
where in the neighborhood of
∂˜Δ∂ℜ0|a=0,ℜ0=RH0=3R2H0[bK(c+d+γ)2−bcK2μ]+2RH0[b2K(c+d+γ)+bcK2μ]=−RH0[b2K(c+d+γ)+bcK2μ]≠0. | (28) |
then by the Implicit Function Theorem, there exists a unique smooth function
˜Δ(a.ℜ0(a))=˜Δ(a,RH0+aRH1+O(a2))=(R3H0+3aR2H0RH1)[bK(c+d+γ)2(1+2abμ)+2cK2ab(c+d+γ)+bcμK2(abμ−1)]+(R2H0+2aRH0RH1)[−2ab2K(c+d+γ)2μ+b2K(c+d+γ)(1+3abμ)−2abcK2(c+d+γ)−ab2cK2+bμcK2]+(RH0+aRH1)[−3ab3K(c+d+γ)μ]=0 | (29) |
Equalizing the same power terms of parameter
3R2H0RH1[bK(c+d+γ)2−bμcK2]+R3H0[2b2K(c+d+γ)2μ+2bcK2(c+d+γ)+b2cK2]+2RH0RH1[b2K(c+d+γ)+bμcK2] |
+R2H0[−2b2K(c+d+γ)2μ+3b3K(c+d+γ)μ−2bcK2(c+d+γ)−b2cK2]+RH0[−3b3K(c+d+γ)μ]=0 | (30) |
thus we solve
Theorem 4.4. Consider model (2). If
Proof. When
a0=μcbS∗ℜ0+bc(2S∗K−1)⋅(μKℜ0−2μK2ℜ20S∗)=μcbℜ0S∗⋅(3S∗2−KS∗−4KS∗ℜ0+2K2ℜ0)=μcbK2ℜ20S∗⋅[(1−1ℜ0)(1+2abℜ0μ−abμ)+O(a2)]. | (31) |
if
Next, we prove
a2a1−a0=(c+d+γ+bS∗K)⋅[bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗]−[μcbS∗ℜ0+bc(2S∗K−1)⋅(μKℜ0−2μK2ℜ20S∗)]=bKℜ50S∗⋅[ℜ30(Δ2−μcK+T1a)+ℜ20(bΔ+μcK−T1aT2a)−ℜ0T2a+T2a+O(a2)]=bKℜ50S∗⋅[ℜ30(Δ2−μcK)+ℜ20(bΔ+μcK)+ℜ20T1a(ℜ0−1)+ℜ0T2a(ℜ0−1)]>0 | (32) |
where
Theorem 4.5. Consider model (2). If
Proof. Differentiating (16) with respect
dλdμ=−dS∗dμ⋅B1B2, | (33) |
where
B1=bKλ2+[bK(c+d+γ)+2Kr(c+d)ℜ0S∗2]λ+bγ(c+d)(3K−2Kℜ0S∗2),B2=3λ2+2(c+d+γ+bS∗K)⋅λ+bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗. | (34) |
When
S∗=γ(c+d)μc+ab2c(K−S∗)2S∗2μK2γ(c+d), |
so
dS∗dμ=−S∗μ+2ab2c(K−S∗)(K−2S∗)S∗μK2γ(c+d)⋅dS∗dμ, |
dS∗dμ=−bcS(K−S)ℜ0a0. |
Hence we have
sign{d(Reλ)dμ}λ=iω=sign{Re(dλdμ)}λ=iω=sign{Re(bKω2−[bK(c+d+γ)+2Kγ(c+d)ℜ0S∗2]⋅iω−bγ(c+d)(3K−2Kℜ0S∗2)−3ω2+2(c+d+γ+bS∗K)⋅iω+bS∗K(c+d+γ)+2μcKℜ0−2μcK2ℜ20S∗)}=sign{Re(bKω2−[bK(c+d+γ)+2Kγ(c+d)ℜ0S∗2]⋅iω−bγ(c+d)(3K−2Kℜ0S∗2))×(−2ω2−2(c+d+γ+bS∗K)⋅iω)}=sign{2bKω4+2ω2[bK(γ−c+d2)2+3(c+d)24+cd]+(c+d+γ)b2S∗K2+(c+d+γ+b+bS∗K)2Kγ(c+d)ℜ0S∗2]}>0. | (35) |
Therefore, the system undergoes a Hopf bifurcation when
To analyze our results, we provide numerical examples in this section.
We choose parameter a from Table 1. The other parameters K is 5000000 people, b is selected as 0.001
Parameter a | | | |
| 4208333 | 6597 | 13194 |
| 4215551 | 6548 | 13096 |
| 4272153 | 6157 | 12314 |
First, we consider the case where the removal rate from the infected compartment is relatively higher, that is
Fig. 2 (a), (b) simulate the media impact to the transmission when
Fig. 3 describes the change of the maximum infected individuals when
In this paper, we explore the impact of media coverage
We derive formulas for the basic reproductive number of infection
From the numerical simulations, we obtain that the media coverage
T_0=\frac{2\pi }{\omega} =\frac{2\pi }{\sqrt{\frac{b }{\Re_0}(c+d+\gamma)}}. |
But when the media impact parameter
T_a=\frac{2\pi }{\sqrt{\frac{b(c+d+\gamma) }{\Re_0}+a\frac{b^2(c+d+\gamma) } {\mu \Re_0} } (1-\frac{1}{\Re_0})+\frac{2\mu cK}{\Re_0}(1-\frac{1}{1+a\frac{b}{\mu}(1-\frac{1}{\Re_0})})} |
This shows that the media alert shortens the time of the secondary peak and trough of the disease transmission. This effect is also verified by the simulations in Fig. 2 (a), (b).
For the case where
The authors are grateful to the editor and the anonymous reviewers for their valuable comments and suggestions, based on which they revised this manuscript. XL and SL are supported by the NNSF of China (No. 11471089,11301453) and the Fundamental Research Funds for the Central Universities (Grant No. HIT. IBRSEM. A. 201401). JL is supported partially by U.S. National Science Foundation grant DMS-1118150.
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Parameter a | | | |
| 4208333 | 6597 | 13194 |
| 4215551 | 6548 | 13096 |
| 4272153 | 6157 | 12314 |